A309043 - OEIS

%I #6 Jul 09 2019 11:12:36

%S 1,2,5,6,12,14,23,22,35,36,56,52,77,74,105,90,124,114,163,142,199,184,

%T 256,216,289,258,357,302,404,358,479,390,499,428,576,476,629,554,745,

%U 610,788,682,923,766,1007,880,1168,944,1193,1010,1341,1094,1420,1230,1631,1318,1667

%N Expansion of Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)))^2.

%F G.f.: Product_{k>=0} ((1 - x^(3*2^k))/(1 - x^(2^k)))^2.

%F G.f. A(x) satisfies: A(x) = (1 + x + x^2)^2 * A(x^2).

%F a(n) = Sum_{k=0..n} A002487(k+1)*A002487(n-k+1).

%t nmax = 56; CoefficientList[Series[Product[(1 + x^(2^k) + x^(2^(k + 1)))^2, {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

%t nmax = 56; A[_] = 1; Do[A[x_] = (1 + x + x^2)^2 A[x^2] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%Y Cf. A002487, A073469, A171238, A185954, A309044.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Jul 09 2019