A173677 - OEIS

%I #20 Nov 10 2023 12:26:26

%S 1,2,1,0,0,0,0,0,2,2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,

%T 0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,2,0,0,

%U 0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2

%N Number of ways of writing n as a sum of two nonnegative cubes.

%C Order matters. This is the coefficient of q^n in the expansion of {Sum_{m>=0} q^(m^3)}^2.

%H Seiichi Manyama, <a href="/A173677/b173677.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k=0..n} c(k) * c(n-k), where c = A010057. - _Wesley Ivan Hurt_, Nov 09 2023

%o (PARI) list(n)=my(q='q);Vec(sum(m=0,(n+.5)^(1/3),q^(m^3),O(q^(n+1)))^2) \\ _Charles R Greathouse IV_, Jun 07 2012

%Y Cf. A004829, A008451, A010057, A051343, A173676.

%Y Sums of k cubes, number of ways of writing n as, for k=1..9: A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 24 2010