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%I #12 Aug 24 2019 11:50:55
%S 1,1,2,4,6,8,13,12,20,24,25,29,49,40,50,64,86,80,105,102,164,175,186,
%T 208,325,316,382,476,624,660,814,961,1331,1500,1739,2140,2877,3274,
%U 3939,4901,6345,7448,9054,11157,14315,17181,20769,25843,32947,39639,48257,60075
%N Number of compositions of n with equal differences up to sign.
%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 Andrew Howroyd, <a href="/A325557/b325557.txt">Table of n, a(n) for n = 0..200</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(8) = 20 compositions:
%e (1) (2) (3) (4) (5) (6) (7) (8)
%e (11) (12) (13) (14) (15) (16) (17)
%e (21) (22) (23) (24) (25) (26)
%e (111) (31) (32) (33) (34) (35)
%e (121) (41) (42) (43) (44)
%e (1111) (131) (51) (52) (53)
%e (212) (123) (61) (62)
%e (11111) (141) (151) (71)
%e (222) (232) (161)
%e (321) (313) (242)
%e (1212) (12121) (323)
%e (2121) (1111111) (1232)
%e (111111) (1313)
%e (2123)
%e (2222)
%e (2321)
%e (3131)
%e (3212)
%e (21212)
%e (11111111)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],SameQ@@Abs[Differences[#]]&]],{n,0,15}]
%o (PARI)
%o step(R,n,s)={matrix(n, n, i, j, if(i>j, if(j>s, R[i-j, j-s]) + if(j+s<=n, R[i-j, j+s])) )}
%o w(n,s)={my(R=matid(n), t=0); while(R, R=step(R,n,s); t+=vecsum(R[n,])); t}
%o a(n) = {numdiv(max(1,n)) + sum(s=1, n-1, w(n,s))} \\ _Andrew Howroyd_, Aug 22 2019
%Y Cf. A000079, A047966, A049988, A070211, A098504, A173258, A175342, A325545, A325546, A325547, A325548, A325552, A325558.
%K nonn
%O 0,3
%A _Gus Wiseman_, May 11 2019
%E a(26)-a(42) from _Lars Blomberg_, May 30 2019
%E Terms a(43) and beyond from _Andrew Howroyd_, Aug 22 2019
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