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A175365
Number of integer triples (x,y,z) satisfying |x|^3 + |y|^3 + |z|^3 = n, -n <= x,y,z <= n.
5
1, 6, 12, 8, 0, 0, 0, 0, 6, 24, 24, 0, 0, 0, 0, 0, 12, 24, 0, 0, 0, 0, 0, 0, 8, 0, 0, 6, 24, 24, 0, 0, 0, 0, 0, 24, 48, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 24, 0, 0, 0, 0, 0, 0, 24, 0, 6, 24, 24, 0, 0, 0, 0, 0, 24, 48, 0, 0, 0, 0, 0, 0, 24, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 48, 0, 0, 0
OFFSET
0,2
COMMENTS
A three-dimensional variant of A175362.
LINKS
FORMULA
G.f.: ( 1 + 2*Sum_{j>=1} x^(j^3) )^3.
a(n) = A175362(n) + 2*Sum_{k=1..floor(n^(1/3))} A175362(n - k^3). - Daniel Suteu, Aug 15 2021
EXAMPLE
a(2) = 12 counts (x,y,z) = (-1,-1,0), (-1,0,-1), (-1,0,1), (-1,1,0), (0,-1,-1), (0,-1,1), (0,1,-1), (0,1,1), (1,-1,0), (1,0,-1), (1,0,1) and (1,1,0).
MAPLE
N:= 100: # to get a(0) to a(N)
G:= (1+2*add(x^(j^3), j=1..floor(N^(1/3))))^3:
S:= series(G, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Apr 08 2016
MATHEMATICA
CoefficientList[(1 + 2 Sum[x^(j^3), {j, 4}])^3, x] (* Michael De Vlieger, Apr 08 2016 *)
PROG
(PARI) a(n, k=3) = 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
Sequence in context: A295122 A103698 A175375 * A029769 A074590 A272966
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 24 2010
STATUS
approved