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 A325548 Number of compositions of n with strictly decreasing differences. 12
 1, 1, 2, 3, 5, 8, 10, 13, 19, 23, 29, 38, 46, 55, 69, 80, 96, 115, 132, 154, 183, 207, 238, 276, 314, 356, 405, 455, 513, 579, 647, 724, 809, 897, 998, 1107, 1225, 1350, 1486, 1639, 1805, 1973, 2166, 2374, 2586, 2824, 3084, 3346, 3646, 3964, 4286, 4655, 5047 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts. EXAMPLE The a(1) = 1 through a(8) = 19 compositions: (1) (2) (3) (4) (5) (6) (7) (8) (11) (12) (13) (14) (15) (16) (17) (21) (22) (23) (24) (25) (26) (31) (32) (33) (34) (35) (121) (41) (42) (43) (44) (122) (51) (52) (53) (131) (132) (61) (62) (221) (141) (133) (71) (231) (142) (134) (1221) (151) (143) (232) (152) (241) (161) (331) (233) (242) (251) (332) (341) (431) (1331) MAPLE b:= proc(n, l, d) option remember; `if`(n=0, 1, add(`if`(l=0 or j-l b(n, 0\$2): seq(a(n), n=0..52); # Alois P. Heinz, Jan 27 2024 MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Greater@@Differences[#]&]], {n, 0, 15}] CROSSREFS Cf. A011782, A000740, A008965, A070211, A175342, A179254, A320470, A325457, A325545, A325546, A325547, A325552, A325557. Sequence in context: A186498 A226330 A226329 * A094568 A251607 A219276 Adjacent sequences: A325545 A325546 A325547 * A325549 A325550 A325551 KEYWORD nonn AUTHOR Gus Wiseman, May 10 2019 EXTENSIONS a(26)-a(44) from Lars Blomberg, May 30 2019 a(45)-a(52) from Alois P. Heinz, Jan 27 2024 STATUS approved

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Last modified July 20 18:09 EDT 2024. Contains 374459 sequences. (Running on oeis4.)