A281155 - OEIS

%I #4 Jan 16 2017 14:19:14

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,3,0,3,0,0,1,0,6,0,0,0,3,

%T 3,0,3,0,6,0,0,3,0,3,3,6,0,0,1,6,6,0,0,0,6,0,6,6,0,3,0,6,6,0,0,6,3,3,

%U 3,6,6,0,3,0,6,1,3,12,6,0,0,6,3,6,6,0,3,0,3,15,6,0,0,6,12,0,3,3,6,6,0,12,3,0,6,6

%N Expansion of (Sum_{k>=2} x^(k^2))^3.

%C Number of ways to write n as an ordered sum of 3 squares > 1.

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F G.f.: (Sum_{k>=2} x^(k^2))^3.

%F G.f.: (1/8)*(-1 - 2*x + theta_3(0,x))^3, where theta_3 is the 3rd Jacobi theta function.

%e G.f. = x^12 + 3*x^17 + 3*x^22 + 3*x^24 + x^27 + 6*x^29 + 3*x^33 + 3*x^34 + 3*x^36 + ...

%e a(17) = 3 because we have [9, 4, 4], [4, 9, 4] and [4, 4, 9].

%t nmax = 105; CoefficientList[Series[Sum[x^k^2, {k, 2, nmax}]^3, {x, 0, nmax}], x]

%t CoefficientList[Series[(-1 - 2 x + EllipticTheta[3, 0, x])^3/8, {x, 0, 105}], x]

%Y Cf. A000290, A005875, A002102, A006456, A063691, A078134, A280542.

%K nonn

%O 0,18

%A _Ilya Gutkovskiy_, Jan 16 2017