OFFSET
0,2
COMMENTS
A variant of A000118 with cubes instead of squares.
LINKS
Daniel Suteu, Table of n, a(n) for n = 0..10000
FORMULA
Conjectured g.f.: (1 + 2*Sum_{j>=1} x^(j^3))^4.
EXAMPLE
a(1) = 8 counts (x,y,z,u) = (-1,0,0,0), (0,-1,0,0), (0,0,-1,0), (0,0,0,-1) and 4 more tuples with -1 replaced by +1.
a(2) = 24 counts (x,y,z,u) = (-1,-1,0,0), (-1,0,-1,0), (-1,0,0,-1), (-1,0,0,1) etc, all variants where two of the 4 values are zero and the other two +1 or -1.
PROG
(PARI) a(n, k=4) = if(n==0, return(1)); if(k <= 0, return(0)); if(k == 1, return(ispower(n, 3))); my(count = 0); for(v = 0, sqrtnint(n, 3), count += (2 - (v == 0))*if(k > 2, a(n - v^3, k-1), if(ispower(n - v^3, 3), 2 - (n - v^3 == 0), 0))); count; \\ Daniel Suteu, Aug 15 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 24 2010
STATUS
approved