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%I #67 Sep 18 2013 12:32:17
%S 1,2,4,6,8,12,16,22,24,28,32,44,48,56,64,86,88,92,96,112,120,128,172,
%T 176,184,192,220,224,240,256,342,344,348,352,368,376,384,440,448,480,
%U 496,512,684,688,696,704,732,736,752,768,880,888,896,960,992,1024
%N Indices (k) of partitions in the list of compositions of j in colexicographic order, if 1<=k<=2^(j-1), j>=1.
%C Also where records occur in A228720.
%C 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.
%C The total number of terms in the first j rows of triangle is A000041(j), j >= 1.
%C Row j has length A187219(j).
%C Right border gives A000079.
%F a(n) = 1 + A194602(n-1).
%F A001511(a(n)) = A141285(n).
%F A000120(a(n)-1) = A207034(n).
%e 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:
%e ---------------------------------------------------------
%e . Compositions Partitions
%e k of 5 of 5 n a(n)
%e ---------------------------------------------------------
%e 1 1+1+1+1+1 * ............... * 1+1+1+1+1 1 1
%e 2 2+1+1+1 * ............... * 2+1+1+1 2 2
%e 3 1+2+1+1 ........... * 3+1+1 3 4
%e 4 3+1+1 * .../ .......... * 2+2+1 4 6
%e 5 1+1+2+1 / ......... * 4+1 5 8
%e 6 2+2+1 * .../ / ...... * 3+2 6 12
%e 7 1+3+1 / / ... * 5 7 16
%e 8 4+1 * .../ / /
%e 9 1+1+1+2 / /
%e 10 2+1+2 / /
%e 11 1+2+2 / /
%e 12 3+2 * .../ /
%e 13 1+1+3 /
%e 14 2+3 /
%e 15 1+4 /
%e 16 5 * .../
%e .
%e Written as an irregular triangle the sequence begins:
%e 1;
%e 2;
%e 4;
%e 6,8;
%e 12,16;
%e 22,24,28,32;
%e 44,48,56,64;
%e 86,88,92,96,112,120,128;
%e 172,176,184,192,220,224,240,256;
%e 342,344,348,352,368,376,384,440,448,480,496,512;
%e 684,688,696,704,732,736,752,768,880,888,896,960,992,1024;
%e ...
%Y Cf. A000041, A187219, A211992, A228354, A228525, A228720.
%K nonn,tabf
%O 1,2
%A _Omar E. Pol_, Aug 20 2013
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