%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