A309043 Expansion of Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)))^2.

1, 2, 5, 6, 12, 14, 23, 22, 35, 36, 56, 52, 77, 74, 105, 90, 124, 114, 163, 142, 199, 184, 256, 216, 289, 258, 357, 302, 404, 358, 479, 390, 499, 428, 576, 476, 629, 554, 745, 610, 788, 682, 923, 766, 1007, 880, 1168, 944, 1193, 1010, 1341, 1094, 1420, 1230, 1631, 1318, 1667

Offset

0,2

Links

Table of n, a(n) for n=0..56.

Formula

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

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

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

Mathematica

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]
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]

Crossrefs

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

Sequence in context: A289206 A153485 A244048 * A023143 A085206 A238481

Adjacent sequences: A309040 A309041 A309042 * A309044 A309045 A309046

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 09 2019

Status

approved