Decomposition of Flag numbers - 2D graph - First 500 terms
"Flag numbers": number of dots that can be arranged in successive rows of K, K-1, K, K-1, K, ..., K-1, K (assuming there is a total of L > 1 rows of size K > 1).
n |
a053726 |
weight k(n) |
level L(n) |
jump |
1 |
5 |
0 |
0 |
3 |
2 |
8 |
5 |
1 |
3 |
3 |
11 |
3 |
3 |
2 |
4 |
13 |
2 |
6 |
1 |
5 |
14 |
11 |
1 |
3 |
6 |
17 |
2 |
8 |
1 |
7 |
18 |
4 |
4 |
2 |
8 |
20 |
17 |
1 |
3 |
9 |
23 |
3 |
7 |
2 |
10 |
25 |
2 |
12 |
1 |
11 |
26 |
3 |
8 |
2 |
12 |
28 |
3 |
9 |
1 |
13 |
29 |
13 |
2 |
3 |
14 |
32 |
31 |
1 |
1 |
15 |
33 |
31 |
1 |
2 |
16 |
35 |
4 |
8 |
3 |
17 |
38 |
37 |
1 |
1 |
18 |
39 |
37 |
1 |
2 |
19 |
41 |
3 |
13 |
2 |
20 |
43 |
2 |
21 |
1 |
21 |
44 |
3 |
14 |
2 |
22 |
46 |
3 |
15 |
1 |
23 |
47 |
2 |
23 |
1 |
24 |
48 |
23 |
2 |
2 |
25 |
50 |
47 |
1 |
3 |
26 |
53 |
5 |
10 |
3 |
27 |
56 |
3 |
18 |
2 |
28 |
58 |
3 |
19 |
1 |
29 |
59 |
2 |
29 |
1 |
30 |
60 |
59 |
1 |
1 |
31 |
61 |
2 |
30 |
1 |
32 |
62 |
61 |
1 |
1 |
33 |
63 |
61 |
1 |
2 |
34 |
65 |
3 |
21 |
2 |
35 |
67 |
2 |
33 |
1 |
36 |
68 |
5 |
13 |
3 |
37 |
71 |
2 |
35 |
1 |
38 |
72 |
71 |
1 |
1 |
39 |
73 |
2 |
36 |
1 |
40 |
74 |
71 |
1 |
3 |
41 |
77 |
2 |
38 |
1 |
42 |
78 |
4 |
19 |
2 |
43 |
80 |
79 |
1 |
1 |
44 |
81 |
79 |
1 |
2 |
45 |
83 |
3 |
27 |
2 |
46 |
85 |
2 |
42 |
1 |
47 |
86 |
3 |
28 |
2 |
48 |
88 |
3 |
29 |
1 |
49 |
89 |
43 |
2 |
3 |
50 |
92 |
7 |
13 |
1 |
51 |
93 |
2 |
46 |
1 |
52 |
94 |
3 |
31 |
1 |
53 |
95 |
4 |
23 |
3 |
54 |
98 |
5 |
19 |
3 |
55 |
101 |
2 |
50 |
1 |
56 |
102 |
101 |
1 |
1 |
57 |
103 |
2 |
51 |
1 |
58 |
104 |
103 |
1 |
1 |
59 |
105 |
103 |
1 |
2 |
60 |
107 |
2 |
53 |
1 |
61 |
108 |
107 |
1 |
1 |
62 |
109 |
2 |
54 |
1 |
63 |
110 |
109 |
1 |
1 |
64 |
111 |
109 |
1 |
2 |
65 |
113 |
5 |
22 |
3 |
66 |
116 |
3 |
38 |
2 |
67 |
118 |
3 |
39 |
1 |
68 |
119 |
4 |
29 |
3 |
69 |
122 |
11 |
11 |
1 |
70 |
123 |
2 |
61 |
1 |
71 |
124 |
3 |
41 |
1 |
72 |
125 |
3 |
41 |
2 |
73 |
127 |
2 |
63 |
1 |
74 |
128 |
3 |
42 |
2 |
75 |
130 |
3 |
43 |
1 |
76 |
131 |
3 |
43 |
2 |
77 |
133 |
2 |
66 |
1 |
78 |
134 |
131 |
1 |
3 |
79 |
137 |
2 |
68 |
1 |
80 |
138 |
4 |
34 |
2 |
81 |
140 |
137 |
1 |
3 |
82 |
143 |
2 |
71 |
1 |
83 |
144 |
11 |
13 |
1 |
84 |
145 |
2 |
72 |
1 |
85 |
146 |
3 |
48 |
2 |
86 |
148 |
3 |
49 |
1 |
87 |
149 |
2 |
74 |
1 |
88 |
150 |
149 |
1 |
1 |
89 |
151 |
2 |
75 |
1 |
90 |
152 |
151 |
1 |
1 |
91 |
153 |
151 |
1 |
2 |
92 |
155 |
4 |
38 |
3 |
93 |
158 |
3 |
52 |
2 |
94 |
160 |
3 |
53 |
1 |
95 |
161 |
2 |
80 |
1 |
96 |
162 |
7 |
23 |
1 |
97 |
163 |
2 |
81 |
1 |
98 |
164 |
163 |
1 |
1 |
99 |
165 |
163 |
1 |
2 |
100 |
167 |
2 |
83 |
1 |
101 |
168 |
83 |
2 |
2 |
102 |
170 |
13 |
13 |
1 |
103 |
171 |
2 |
85 |
1 |
104 |
172 |
3 |
57 |
1 |
105 |
173 |
5 |
34 |
3 |
106 |
176 |
3 |
58 |
2 |
107 |
178 |
3 |
59 |
1 |
108 |
179 |
3 |
59 |
2 |
109 |
181 |
2 |
90 |
1 |
110 |
182 |
181 |
1 |
1 |
111 |
183 |
181 |
1 |
2 |
112 |
185 |
2 |
92 |
1 |
113 |
186 |
4 |
46 |
2 |
114 |
188 |
11 |
17 |
1 |
115 |
189 |
11 |
17 |
2 |
116 |
191 |
3 |
63 |
2 |
117 |
193 |
2 |
96 |
1 |
118 |
194 |
3 |
64 |
2 |
119 |
196 |
3 |
65 |
1 |
120 |
197 |
2 |
98 |
1 |
121 |
198 |
4 |
49 |
2 |
122 |
200 |
3 |
66 |
2 |
123 |
202 |
3 |
67 |
1 |
124 |
203 |
2 |
101 |
1 |
125 |
204 |
101 |
2 |
2 |
126 |
206 |
5 |
41 |
1 |
127 |
207 |
2 |
103 |
1 |
128 |
208 |
3 |
69 |
1 |
129 |
209 |
103 |
2 |
3 |
130 |
212 |
211 |
1 |
1 |
131 |
213 |
2 |
106 |
1 |
132 |
214 |
3 |
71 |
1 |
133 |
215 |
4 |
53 |
3 |
134 |
218 |
7 |
31 |
1 |
135 |
219 |
7 |
31 |
2 |
136 |
221 |
3 |
73 |
2 |
137 |
223 |
2 |
111 |
1 |
138 |
224 |
3 |
74 |
2 |
139 |
226 |
3 |
75 |
1 |
140 |
227 |
2 |
113 |
1 |
141 |
228 |
113 |
2 |
2 |
142 |
230 |
227 |
1 |
3 |
143 |
233 |
3 |
77 |
2 |
144 |
235 |
2 |
117 |
1 |
145 |
236 |
5 |
47 |
1 |
146 |
237 |
2 |
118 |
1 |
147 |
238 |
3 |
79 |
1 |
148 |
239 |
3 |
79 |
2 |
149 |
241 |
2 |
120 |
1 |
150 |
242 |
241 |
1 |
1 |
151 |
243 |
241 |
1 |
2 |
152 |
245 |
3 |
81 |
2 |
153 |
247 |
2 |
123 |
1 |
154 |
248 |
13 |
19 |
1 |
155 |
249 |
13 |
19 |
2 |
156 |
251 |
3 |
83 |
2 |
157 |
253 |
2 |
126 |
1 |
158 |
254 |
3 |
84 |
2 |
159 |
256 |
3 |
85 |
1 |
160 |
257 |
2 |
128 |
1 |
161 |
258 |
257 |
1 |
1 |
162 |
259 |
2 |
129 |
1 |
163 |
260 |
257 |
1 |
3 |
164 |
263 |
2 |
131 |
1 |
165 |
264 |
263 |
1 |
1 |
166 |
265 |
2 |
132 |
1 |
167 |
266 |
5 |
53 |
1 |
168 |
267 |
2 |
133 |
1 |
169 |
268 |
3 |
89 |
1 |
170 |
269 |
2 |
134 |
1 |
171 |
270 |
4 |
67 |
2 |
172 |
272 |
271 |
1 |
1 |
173 |
273 |
271 |
1 |
2 |
174 |
275 |
2 |
137 |
1 |
175 |
276 |
5 |
55 |
1 |
176 |
277 |
2 |
138 |
1 |
177 |
278 |
3 |
92 |
2 |
178 |
280 |
3 |
93 |
1 |
179 |
281 |
3 |
93 |
2 |
180 |
283 |
2 |
141 |
1 |
181 |
284 |
281 |
1 |
3 |
182 |
287 |
2 |
143 |
1 |
183 |
288 |
11 |
26 |
2 |
184 |
290 |
17 |
17 |
1 |
185 |
291 |
2 |
145 |
1 |
186 |
292 |
3 |
97 |
1 |
187 |
293 |
3 |
97 |
2 |
188 |
295 |
2 |
147 |
1 |
189 |
296 |
3 |
98 |
2 |
190 |
298 |
3 |
99 |
1 |
191 |
299 |
4 |
74 |
3 |
192 |
302 |
7 |
43 |
1 |
193 |
303 |
7 |
43 |
2 |
194 |
305 |
2 |
152 |
1 |
195 |
306 |
4 |
76 |
2 |
196 |
308 |
5 |
61 |
3 |
197 |
311 |
2 |
155 |
1 |
198 |
312 |
311 |
1 |
1 |
199 |
313 |
2 |
156 |
1 |
200 |
314 |
313 |
1 |
1 |
201 |
315 |
313 |
1 |
2 |
202 |
317 |
2 |
158 |
1 |
203 |
318 |
317 |
1 |
1 |
204 |
319 |
2 |
159 |
1 |
205 |
320 |
317 |
1 |
3 |
206 |
323 |
3 |
107 |
2 |
207 |
325 |
2 |
162 |
1 |
208 |
326 |
3 |
108 |
2 |
209 |
328 |
3 |
109 |
1 |
210 |
329 |
163 |
2 |
3 |
211 |
332 |
331 |
1 |
1 |
212 |
333 |
2 |
166 |
1 |
213 |
334 |
3 |
111 |
1 |
214 |
335 |
2 |
167 |
1 |
215 |
336 |
167 |
2 |
2 |
216 |
338 |
3 |
112 |
2 |
217 |
340 |
3 |
113 |
1 |
218 |
341 |
3 |
113 |
2 |
219 |
343 |
2 |
171 |
1 |
220 |
344 |
7 |
49 |
1 |
221 |
345 |
7 |
49 |
2 |
222 |
347 |
2 |
173 |
1 |
223 |
348 |
347 |
1 |
1 |
224 |
349 |
2 |
174 |
1 |
225 |
350 |
3 |
116 |
2 |
226 |
352 |
3 |
117 |
1 |
227 |
353 |
2 |
176 |
1 |
228 |
354 |
4 |
88 |
2 |
229 |
356 |
5 |
71 |
1 |
230 |
357 |
2 |
178 |
1 |
231 |
358 |
3 |
119 |
1 |
232 |
359 |
3 |
119 |
2 |
233 |
361 |
2 |
180 |
1 |
234 |
362 |
19 |
19 |
1 |
235 |
363 |
19 |
19 |
2 |
236 |
365 |
2 |
182 |
1 |
237 |
366 |
4 |
91 |
2 |
238 |
368 |
367 |
1 |
1 |
239 |
369 |
367 |
1 |
2 |
240 |
371 |
3 |
123 |
2 |
241 |
373 |
2 |
186 |
1 |
242 |
374 |
373 |
1 |
1 |
243 |
375 |
373 |
1 |
2 |
244 |
377 |
2 |
188 |
1 |
245 |
378 |
4 |
94 |
2 |
246 |
380 |
3 |
126 |
2 |
247 |
382 |
3 |
127 |
1 |
248 |
383 |
2 |
191 |
1 |
249 |
384 |
191 |
2 |
2 |
250 |
386 |
3 |
128 |
2 |
251 |
388 |
3 |
129 |
1 |
252 |
389 |
2 |
194 |
1 |
253 |
390 |
389 |
1 |
1 |
254 |
391 |
2 |
195 |
1 |
255 |
392 |
17 |
23 |
1 |
256 |
393 |
17 |
23 |
2 |
257 |
395 |
2 |
197 |
1 |
258 |
396 |
5 |
79 |
1 |
259 |
397 |
2 |
198 |
1 |
260 |
398 |
3 |
132 |
2 |
261 |
400 |
3 |
133 |
1 |
262 |
401 |
2 |
200 |
1 |
263 |
402 |
401 |
1 |
1 |
264 |
403 |
2 |
201 |
1 |
265 |
404 |
401 |
1 |
3 |
266 |
407 |
2 |
203 |
1 |
267 |
408 |
11 |
37 |
1 |
268 |
409 |
2 |
204 |
1 |
269 |
410 |
11 |
37 |
3 |
270 |
413 |
5 |
82 |
3 |
271 |
416 |
5 |
83 |
1 |
272 |
417 |
2 |
208 |
1 |
273 |
418 |
3 |
139 |
1 |
274 |
419 |
3 |
139 |
2 |
275 |
421 |
2 |
210 |
1 |
276 |
422 |
421 |
1 |
1 |
277 |
423 |
2 |
211 |
1 |
278 |
424 |
3 |
141 |
1 |
279 |
425 |
2 |
212 |
1 |
280 |
426 |
4 |
106 |
2 |
281 |
428 |
5 |
85 |
3 |
282 |
431 |
3 |
143 |
2 |
283 |
433 |
2 |
216 |
1 |
284 |
434 |
433 |
1 |
1 |
285 |
435 |
2 |
217 |
1 |
286 |
436 |
3 |
145 |
1 |
287 |
437 |
2 |
218 |
1 |
288 |
438 |
4 |
109 |
2 |
289 |
440 |
19 |
23 |
3 |
290 |
443 |
3 |
147 |
2 |
291 |
445 |
2 |
222 |
1 |
292 |
446 |
5 |
89 |
1 |
293 |
447 |
2 |
223 |
1 |
294 |
448 |
3 |
149 |
1 |
295 |
449 |
2 |
224 |
1 |
296 |
450 |
449 |
1 |
1 |
297 |
451 |
2 |
225 |
1 |
298 |
452 |
11 |
41 |
1 |
299 |
453 |
11 |
41 |
2 |
300 |
455 |
3 |
151 |
2 |
301 |
457 |
2 |
228 |
1 |
302 |
458 |
457 |
1 |
1 |
303 |
459 |
457 |
1 |
2 |
304 |
461 |
2 |
230 |
1 |
305 |
462 |
461 |
1 |
1 |
306 |
463 |
2 |
231 |
1 |
307 |
464 |
3 |
154 |
2 |
308 |
466 |
3 |
155 |
1 |
309 |
467 |
2 |
233 |
1 |
310 |
468 |
233 |
2 |
2 |
311 |
470 |
3 |
156 |
2 |
312 |
472 |
3 |
157 |
1 |
313 |
473 |
3 |
157 |
2 |
314 |
475 |
2 |
237 |
1 |
315 |
476 |
3 |
158 |
2 |
316 |
478 |
3 |
159 |
1 |
317 |
479 |
2 |
239 |
1 |
318 |
480 |
479 |
1 |
1 |
319 |
481 |
2 |
240 |
1 |
320 |
482 |
13 |
37 |
1 |
321 |
483 |
13 |
37 |
2 |
322 |
485 |
3 |
161 |
2 |
323 |
487 |
2 |
243 |
1 |
324 |
488 |
3 |
162 |
2 |
325 |
490 |
3 |
163 |
1 |
326 |
491 |
3 |
163 |
2 |
327 |
493 |
2 |
246 |
1 |
328 |
494 |
17 |
29 |
1 |
329 |
495 |
17 |
29 |
2 |
330 |
497 |
2 |
248 |
1 |
331 |
498 |
4 |
124 |
2 |
332 |
500 |
499 |
1 |
1 |
333 |
501 |
2 |
250 |
1 |
334 |
502 |
3 |
167 |
1 |
335 |
503 |
2 |
251 |
1 |
336 |
504 |
251 |
2 |
2 |
337 |
506 |
3 |
168 |
2 |
338 |
508 |
3 |
169 |
1 |
339 |
509 |
11 |
46 |
3 |
340 |
512 |
7 |
73 |
1 |
341 |
513 |
2 |
256 |
1 |
342 |
514 |
3 |
171 |
1 |
343 |
515 |
4 |
128 |
3 |
344 |
518 |
11 |
47 |
1 |
345 |
519 |
11 |
47 |
2 |
346 |
521 |
2 |
260 |
1 |
347 |
522 |
521 |
1 |
1 |
348 |
523 |
2 |
261 |
1 |
349 |
524 |
521 |
1 |
3 |
350 |
527 |
2 |
263 |
1 |
351 |
528 |
17 |
31 |
1 |
352 |
529 |
2 |
264 |
1 |
353 |
530 |
17 |
31 |
3 |
354 |
533 |
2 |
266 |
1 |
355 |
534 |
4 |
133 |
2 |
356 |
536 |
5 |
107 |
1 |
357 |
537 |
2 |
268 |
1 |
358 |
538 |
3 |
179 |
1 |
359 |
539 |
2 |
269 |
1 |
360 |
540 |
7 |
77 |
1 |
361 |
541 |
2 |
270 |
1 |
362 |
542 |
541 |
1 |
1 |
363 |
543 |
541 |
1 |
2 |
364 |
545 |
271 |
2 |
3 |
365 |
548 |
3 |
182 |
2 |
366 |
550 |
3 |
183 |
1 |
367 |
551 |
3 |
183 |
2 |
368 |
553 |
2 |
276 |
1 |
369 |
554 |
3 |
184 |
2 |
370 |
556 |
3 |
185 |
1 |
371 |
557 |
2 |
278 |
1 |
372 |
558 |
4 |
139 |
2 |
373 |
560 |
13 |
43 |
1 |
374 |
561 |
13 |
43 |
2 |
375 |
563 |
2 |
281 |
1 |
376 |
564 |
281 |
2 |
2 |
377 |
566 |
5 |
113 |
1 |
378 |
567 |
2 |
283 |
1 |
379 |
568 |
3 |
189 |
1 |
380 |
569 |
2 |
284 |
1 |
381 |
570 |
569 |
1 |
1 |
382 |
571 |
2 |
285 |
1 |
383 |
572 |
571 |
1 |
1 |
384 |
573 |
2 |
286 |
1 |
385 |
574 |
3 |
191 |
1 |
386 |
575 |
4 |
143 |
3 |
387 |
578 |
577 |
1 |
1 |
388 |
579 |
2 |
289 |
1 |
389 |
580 |
3 |
193 |
1 |
390 |
581 |
3 |
193 |
2 |
391 |
583 |
2 |
291 |
1 |
392 |
584 |
11 |
53 |
1 |
393 |
585 |
11 |
53 |
2 |
394 |
587 |
2 |
293 |
1 |
395 |
588 |
587 |
1 |
1 |
396 |
589 |
2 |
294 |
1 |
397 |
590 |
3 |
196 |
2 |
398 |
592 |
3 |
197 |
1 |
399 |
593 |
3 |
197 |
2 |
400 |
595 |
2 |
297 |
1 |
401 |
596 |
3 |
198 |
2 |
402 |
598 |
3 |
199 |
1 |
403 |
599 |
2 |
299 |
1 |
404 |
600 |
13 |
46 |
2 |
405 |
602 |
601 |
1 |
1 |
406 |
603 |
2 |
301 |
1 |
407 |
604 |
3 |
201 |
1 |
408 |
605 |
2 |
302 |
1 |
409 |
606 |
4 |
151 |
2 |
410 |
608 |
3 |
202 |
2 |
411 |
610 |
3 |
203 |
1 |
412 |
611 |
3 |
203 |
2 |
413 |
613 |
2 |
306 |
1 |
414 |
614 |
13 |
47 |
3 |
415 |
617 |
2 |
308 |
1 |
416 |
618 |
4 |
154 |
2 |
417 |
620 |
619 |
1 |
1 |
418 |
621 |
2 |
310 |
1 |
419 |
622 |
3 |
207 |
1 |
420 |
623 |
2 |
311 |
1 |
421 |
624 |
311 |
2 |
2 |
422 |
626 |
5 |
125 |
1 |
423 |
627 |
2 |
313 |
1 |
424 |
628 |
3 |
209 |
1 |
425 |
629 |
3 |
209 |
2 |
426 |
631 |
2 |
315 |
1 |
427 |
632 |
631 |
1 |
1 |
428 |
633 |
2 |
316 |
1 |
429 |
634 |
3 |
211 |
1 |
430 |
635 |
2 |
317 |
1 |
431 |
636 |
5 |
127 |
1 |
432 |
637 |
2 |
318 |
1 |
433 |
638 |
5 |
127 |
3 |
434 |
641 |
3 |
213 |
2 |
435 |
643 |
2 |
321 |
1 |
436 |
644 |
641 |
1 |
3 |
437 |
647 |
2 |
323 |
1 |
438 |
648 |
17 |
38 |
2 |
439 |
650 |
647 |
1 |
3 |
440 |
653 |
3 |
217 |
2 |
441 |
655 |
2 |
327 |
1 |
442 |
656 |
5 |
131 |
1 |
443 |
657 |
2 |
328 |
1 |
444 |
658 |
3 |
219 |
1 |
445 |
659 |
4 |
164 |
3 |
446 |
662 |
661 |
1 |
1 |
447 |
663 |
661 |
1 |
2 |
448 |
665 |
2 |
332 |
1 |
449 |
666 |
5 |
133 |
1 |
450 |
667 |
2 |
333 |
1 |
451 |
668 |
23 |
29 |
1 |
452 |
669 |
2 |
334 |
1 |
453 |
670 |
3 |
223 |
1 |
454 |
671 |
2 |
335 |
1 |
455 |
672 |
11 |
61 |
1 |
456 |
673 |
2 |
336 |
1 |
457 |
674 |
673 |
1 |
1 |
458 |
675 |
2 |
337 |
1 |
459 |
676 |
3 |
225 |
1 |
460 |
677 |
2 |
338 |
1 |
461 |
678 |
677 |
1 |
1 |
462 |
679 |
2 |
339 |
1 |
463 |
680 |
3 |
226 |
2 |
464 |
682 |
3 |
227 |
1 |
465 |
683 |
3 |
227 |
2 |
466 |
685 |
2 |
342 |
1 |
467 |
686 |
3 |
228 |
2 |
468 |
688 |
3 |
229 |
1 |
469 |
689 |
2 |
344 |
1 |
470 |
690 |
4 |
172 |
2 |
471 |
692 |
691 |
1 |
1 |
472 |
693 |
2 |
346 |
1 |
473 |
694 |
3 |
231 |
1 |
474 |
695 |
2 |
347 |
1 |
475 |
696 |
5 |
139 |
1 |
476 |
697 |
2 |
348 |
1 |
477 |
698 |
17 |
41 |
1 |
478 |
699 |
17 |
41 |
2 |
479 |
701 |
2 |
350 |
1 |
480 |
702 |
701 |
1 |
1 |
481 |
703 |
2 |
351 |
1 |
482 |
704 |
3 |
234 |
2 |
483 |
706 |
3 |
235 |
1 |
484 |
707 |
2 |
353 |
1 |
485 |
708 |
7 |
101 |
1 |
486 |
709 |
2 |
354 |
1 |
487 |
710 |
709 |
1 |
1 |
488 |
711 |
709 |
1 |
2 |
489 |
713 |
5 |
142 |
3 |
490 |
716 |
3 |
238 |
2 |
491 |
718 |
3 |
239 |
1 |
492 |
719 |
3 |
239 |
2 |
493 |
721 |
2 |
360 |
1 |
494 |
722 |
7 |
103 |
1 |
495 |
723 |
7 |
103 |
2 |
496 |
725 |
19 |
38 |
3 |
497 |
728 |
727 |
1 |
1 |
498 |
729 |
727 |
1 |
2 |
499 |
731 |
2 |
365 |
1 |
500 |
732 |
17 |
43 |
1 |