A309045 Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) + x^(3^(k+1)))^(2^k).

1, 1, 1, 3, 2, 2, 5, 3, 3, 11, 8, 8, 19, 11, 11, 25, 14, 14, 41, 27, 27, 59, 32, 32, 70, 38, 38, 110, 72, 72, 158, 86, 86, 190, 104, 104, 289, 185, 185, 395, 210, 210, 455, 245, 245, 645, 400, 400, 829, 429, 429, 915, 486, 486, 1269, 783, 783, 1623, 840, 840, 1800, 960, 960, 2472

Offset: 0

Author

Ilya Gutkovskiy, Jul 09 2019

Keywords

• nonn

Comments

The trisection equals the self-convolution of this sequence.

Crossrefs

Cf. A054390, A237651, A309046.

Programs

Mathematica

nmax = 63; CoefficientList[Series[Product[(1 + x^(3^k) + x^(2 3^k) + x^(3^(k + 1)))^(2^k), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]
nmax = 63; A[] = 1; Do[A[x] = (1 + x + x^2 + x^3) A[x^3]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f.: Product_{k>=0} ((1 - x^(4*3^k))/(1 - x^(3^k)))^(2^k).

G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3) * A(x^3)^2.