OFFSET
0,2
COMMENTS
Cube variant of A004018.
Obviously, a(n) must be 4*k, for k >= 0, n > 0. - Altug Alkan, Apr 09 2016
From Robert Israel, Jan 26 2017: (Start)
a(k^3*n) >= a(n) for k >= 1.
a(n) >= 16 for n in A001235.
a(A011541(n)) >= 8*n. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: ( 1 + 2 * Sum_{j>=1} x^(j^3) )^2.
a(n^3) = 4 for n > 0. - Altug Alkan, Apr 09 2016
a(n) = 4*Sum_{k=1..floor(n^(1/3))} A010057(n - k^3), for n > 0. - Daniel Suteu, Aug 15 2021
EXAMPLE
a(2) = 4 counts (x,y) = (-1,1), (1,1), (-1,-1) and (1,-1).
a(9) = 8 counts (x,y) = (-2,-1), (-2,1), (-1,-2), (-1,2), (1,-2), (1,2), (2,-1) and (2,1).
MAPLE
N:= 200: # to get a(0)..a(N)
G:= (1+2*add(x^(j^3), j=1..floor(N^(1/3))))^2:
seq(coeff(G, x, j), j=0..N); # Robert Israel, Jan 26 2017
PROG
(PARI) a(n) = if(n==0, 1, 4*sum(k=1, sqrtnint(n, 3), ispower(n - k^3, 3))); \\ Daniel Suteu, Aug 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 24 2010
EXTENSIONS
Invalid claim that belonged to A004018 removed by R. J. Mathar, Apr 24 2010
STATUS
proposed