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 A357487 Number of integer partitions of n with the same length as reverse-alternating sum. 11
 1, 1, 0, 0, 0, 1, 0, 2, 0, 4, 0, 5, 0, 9, 0, 13, 0, 23, 0, 34, 0, 54, 0, 78, 0, 120, 0, 170, 0, 252, 0, 358, 0, 517, 0, 725, 0, 1030, 0, 1427, 0, 1992, 0, 2733, 0, 3759, 0, 5106, 0, 6946, 0, 9345, 0, 12577, 0, 16788, 0, 22384, 0, 29641, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS A partition of n is a weakly decreasing sequence of positive integers summing to n. The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i. LINKS Table of n, a(n) for n=0..60. EXAMPLE The a(1) = 1 through a(13) = 9 partitions: 1 . . . 311 . 322 . 333 . 443 . 553 421 432 542 652 531 641 751 51111 52211 52222 62111 53311 62221 63211 73111 7111111 MATHEMATICA ats[y_]:=Sum[(-1)^(i-1)*y[[i]], {i, Length[y]}]; Table[Length[Select[IntegerPartitions[n], Length[#]==ats[Reverse[#]]&]], {n, 0, 30}] CROSSREFS For product equal to sum we have A001055, compositions A335405. The version for compositions is A357182, reverse ranked by A357184. The reverse version is A357189, ranked by A357486. These partitions are ranked by A357485. Removing zeros gives A357488. A000041 counts partitions, strict A000009. A025047 counts alternating compositions. A103919 counts partitions by alternating sum, full triangle A344651. A357136 counts compositions by alternating sum, full triangle A097805. Cf. A004526, A051159, A114220, A131044, A262046, A262977, A301987, A357183. Sequence in context: A286663 A114402 A035647 * A225437 A065806 A331185 Adjacent sequences: A357484 A357485 A357486 * A357488 A357489 A357490 KEYWORD nonn AUTHOR Gus Wiseman, Oct 01 2022 STATUS approved

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Last modified August 8 11:12 EDT 2024. Contains 375021 sequences. (Running on oeis4.)