This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325548 #17 Jan 27 2024 15:31:52
%S A325548 1,1,2,3,5,8,10,13,19,23,29,38,46,55,69,80,96,115,132,154,183,207,238,
%T A325548 276,314,356,405,455,513,579,647,724,809,897,998,1107,1225,1350,1486,
%U A325548 1639,1805,1973,2166,2374,2586,2824,3084,3346,3646,3964,4286,4655,5047
%N A325548 Number of compositions of n with strictly decreasing differences.
%C A325548 A composition of n is a finite sequence of positive integers summing to n.
%C A325548 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).
%H A325548 Alois P. Heinz, <a href="/A325548/b325548.txt">Table of n, a(n) for n = 0..400</a>
%H A325548 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325548 The a(1) = 1 through a(8) = 19 compositions:
%e A325548 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325548 (11) (12) (13) (14) (15) (16) (17)
%e A325548 (21) (22) (23) (24) (25) (26)
%e A325548 (31) (32) (33) (34) (35)
%e A325548 (121) (41) (42) (43) (44)
%e A325548 (122) (51) (52) (53)
%e A325548 (131) (132) (61) (62)
%e A325548 (221) (141) (133) (71)
%e A325548 (231) (142) (134)
%e A325548 (1221) (151) (143)
%e A325548 (232) (152)
%e A325548 (241) (161)
%e A325548 (331) (233)
%e A325548 (242)
%e A325548 (251)
%e A325548 (332)
%e A325548 (341)
%e A325548 (431)
%e A325548 (1331)
%p A325548 b:= proc(n, l, d) option remember; `if`(n=0, 1, add(`if`(l=0 or
%p A325548 j-l<d, b(n-j, j, `if`(l=0, infinity, j-l)), 0), j=1..n))
%p A325548 end:
%p A325548 a:= n-> b(n, 0$2):
%p A325548 seq(a(n), n=0..52); # _Alois P. Heinz_, Jan 27 2024
%t A325548 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Greater@@Differences[#]&]],{n,0,15}]
%Y A325548 Cf. A011782, A000740, A008965, A070211, A175342, A179254, A320470, A325457, A325545, A325546, A325547, A325552, A325557.
%K A325548 nonn
%O A325548 0,3
%A A325548 _Gus Wiseman_, May 10 2019
%E A325548 a(26)-a(44) from _Lars Blomberg_, May 30 2019
%E A325548 a(45)-a(52) from _Alois P. Heinz_, Jan 27 2024