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A228354
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Indices (k) of partitions in the list of compositions of j in colexicographic order, if 1<=k<=2^(j-1), j>=1.
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8
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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)
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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 * .../
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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;
...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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