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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. 4
 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 Cf. A000041, A187219, A211992, A228354, A228525, A228720. Sequence in context: A061553 A138934 A008764 * A065386 A048951 A058629 Adjacent sequences:  A228351 A228352 A228353 * A228355 A228356 A228357 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Aug 20 2013 STATUS approved

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Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)