A113263 a(n) is the number of ways the set {1^3, 2^3, ..., n^3} can be partitioned into two sets of equal sums.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 62, 0, 0, 268, 356, 0, 0, 2287, 1130, 0, 0, 5317, 36879, 0, 0, 203016, 319415, 0, 0, 2124580, 1631750, 0, 0, 10953868, 41280525, 0, 0, 242899218, 472958485, 0, 0, 2984270739, 3419746788, 0, 0

Offset

1,15

Comments

a(n)=0 when n == 1 or 2 mod 4.

Links

Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 1..130 (first 100 terms from Alois P. Heinz)

Formula

a(n) is half the coefficient of x^0 in product(x^(k^3)+x^(k^-3), k=1..n).

a(n) = [x^(n^3)] Product_{k=1..n-1} (x^(k^3) + 1/x^(k^3)). - Ilya Gutkovskiy, Feb 01 2024

Maple

A113263:=proc(n) local i, p, t; t:= NULL; p:=1; for i to n do p:=p*(x^(i^3)+x^(-i^3)); t:=t, coeff(p, x, 0)/2; od; t; end;

Mathematica

p = 1; t = {}; Do[p = Expand[p(x^(n^3) + x^(-n^3))]; AppendTo[t, Select[ p, NumberQ[ # ] &]/2], {n, 56}]; t (* Robert G. Wilson v *)

Crossrefs

Cf. A058498, A083527.

Sequence in context: A059431 A289358 A271698 * A063658 A237053 A364022

Adjacent sequences: A113260 A113261 A113262 * A113264 A113265 A113266

Keyword

nonn

Author

Floor van Lamoen, Oct 21 2005

Extensions

More terms from Robert G. Wilson v and Tony Noe, Oct 27 2005

Status

approved