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A228354 Indices (k) of partitions in the list of compositions of j in colexicographic order, if 1<=k<=2^(j-1), j>=1. 8
1, 2, 4, 6, 8, 12, 16, 22, 24, 28, 32, 44, 48, 56, 64, 86, 88, 92, 96, 112, 120, 128, 172, 176, 184, 192, 220, 224, 240, 256, 342, 344, 348, 352, 368, 376, 384, 440, 448, 480, 496, 512, 684, 688, 696, 704, 732, 736, 752, 768, 880, 888, 896, 960, 992, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also where records occur in A228720.
Also triangle read by rows in which row j lists the indices of the partitions of j into parts greater than the smallest part of the partitions of j-1, in the list of compositions of j in colexicographic order. See A228525 and A211992.
The total number of terms in the first j rows of triangle is A000041(j), j >= 1.
Row j has length A187219(j).
Right border gives A000079.
LINKS
FORMULA
a(n) = 1 + A194602(n-1).
A001511(a(n)) = A141285(n).
A000120(a(n)-1) = A207034(n).
EXAMPLE
For j = 5 consider the list of compositions of 5 in colexicographic order (see A228525). The indices of the partitions are 1, 2, 4, 6, 8, 12, 16 which are the first A000041(5) terms of this sequence, see below:
---------------------------------------------------------
. Compositions Partitions
k of 5 of 5 n a(n)
---------------------------------------------------------
1 1+1+1+1+1 * ............... * 1+1+1+1+1 1 1
2 2+1+1+1 * ............... * 2+1+1+1 2 2
3 1+2+1+1 ........... * 3+1+1 3 4
4 3+1+1 * .../ .......... * 2+2+1 4 6
5 1+1+2+1 / ......... * 4+1 5 8
6 2+2+1 * .../ / ...... * 3+2 6 12
7 1+3+1 / / ... * 5 7 16
8 4+1 * .../ / /
9 1+1+1+2 / /
10 2+1+2 / /
11 1+2+2 / /
12 3+2 * .../ /
13 1+1+3 /
14 2+3 /
15 1+4 /
16 5 * .../
.
Written as an irregular triangle the sequence begins:
1;
2;
4;
6,8;
12,16;
22,24,28,32;
44,48,56,64;
86,88,92,96,112,120,128;
172,176,184,192,220,224,240,256;
342,344,348,352,368,376,384,440,448,480,496,512;
684,688,696,704,732,736,752,768,880,888,896,960,992,1024;
...
CROSSREFS
Sequence in context: A061553 A138934 A008764 * A065386 A048951 A326504
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 20 2013
STATUS
approved

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Last modified March 29 02:15 EDT 2024. Contains 371264 sequences. (Running on oeis4.)