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

Author

Floor van Lamoen, Oct 21 2005

Keywords

• nonn

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)

Crossrefs

Cf. A058498, A083527.

Programs

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 *)

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

Extensions

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