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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.

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