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 A113038 Number of ways the set {1,2,...,n} can be split into three subsets of which the sum of one is one more than the equal sums of both other subsets. 1
 0, 0, 0, 1, 0, 0, 5, 0, 0, 60, 0, 0, 747, 0, 0, 11076, 0, 0, 183092, 0, 0, 3238140, 0, 0, 60475317, 0, 0, 1175471401, 0, 0, 23600724220, 0, 0, 486653058995, 0, 0, 10260353188386, 0, 0, 220439819437387, 0, 0, 4813287355239594, 0, 0, 106583271423691692, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..100 FORMULA a(n) is half the coefficient of xy in product(x^(-2k)+x^k(y^k+y^(-k)), k=1..n) for n>1. EXAMPLE For n=7 we have splittings 36/27/145, 36/127/45, 136/27/45, 135/27/46, 126/45/37 so a(7) = 5. MAPLE A113038:=proc(n) local i, j, p, t; t:= 0; for j from 2 to n do p:=1; for i to j do p:=p*(x^(-2*i)+x^i*(y^i+y^(-i))); od; t:=t, coeff(coeff(p, x, 1), y, 1)/2; od; t; end; # second Maple program: b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] \$t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local m; m:= n*(n+1)/2; `if`(m>3 and irem(m, 3)=1, b(((m-1)/3)\$2, (m-1)/3+1, n)/2, 0) end: seq(a(n), n=1..50);  # Alois P. Heinz, Sep 03 2009 CROSSREFS Cf. A112972. Sequence in context: A221361 A083527 A221240 * A082512 A068385 A318657 Adjacent sequences:  A113035 A113036 A113037 * A113039 A113040 A113041 KEYWORD nonn AUTHOR Floor van Lamoen, Oct 12 2005 EXTENSIONS Extended beyond a(25) by Alois P. Heinz, Sep 03 2009 STATUS approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)