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%I #14 Feb 20 2022 20:28:41
%S 1,1,2,3,7,13,17,34,59,105,166,279,442,730,1157,1927,3045,4741,7527,
%T 11667,18048,27928,43334,65861,101385,153404,232287,347643,523721,
%U 780083,1165331,1725966,2561625,3773838,5561577,8151209,11920717,17364461,25269939,36635775
%N Number of compositions of n with distinct differences.
%C A composition of n is a finite sequence of positive integers summing to n.
%C 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 Fausto A. C. Cariboni, <a href="/A325545/b325545.txt">Table of n, a(n) for n = 0..70</a>
%H Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e The a(1) = 1 through a(6) = 17 compositions:
%e (1) (2) (3) (4) (5) (6)
%e (11) (12) (13) (14) (15)
%e (21) (22) (23) (24)
%e (31) (32) (33)
%e (112) (41) (42)
%e (121) (113) (51)
%e (211) (122) (114)
%e (131) (132)
%e (212) (141)
%e (221) (213)
%e (311) (231)
%e (1121) (312)
%e (1211) (411)
%e (1131)
%e (1221)
%e (1311)
%e (2112)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Differences[#]&]],{n,0,15}]
%Y Cf. A000079, A000740, A008965, A059966, A070211, A175342, A242882, A325325, A325352, A325546, A325547, A325548, A325551, A325554.
%K nonn
%O 0,3
%A _Gus Wiseman_, May 10 2019
%E More terms from _Alois P. Heinz_, May 11 2019