

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
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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..nargs1)])[], args[nargs]1)), j=1..nargs1)) end: a:= proc(n) local m; m:= n*(n+1)/2; `if`(m>3 and irem(m, 3)=1, b(((m1)/3)$2, (m1)/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



