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

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