A309046 Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) + x^(3^(k+1)))^(3^k).

1, 1, 1, 4, 3, 3, 9, 6, 6, 25, 19, 19, 58, 39, 39, 105, 66, 66, 211, 145, 145, 394, 249, 249, 630, 381, 381, 1114, 733, 733, 1903, 1170, 1170, 2889, 1719, 1719, 4827, 3108, 3108, 7869, 4761, 4761, 11574, 6813, 6813, 18489, 11676, 11676, 28839, 17163, 17163, 41013, 23850

Offset: 0

Author

Ilya Gutkovskiy, Jul 09 2019

Keywords

• nonn

Comments

The trisection equals the three-fold convolution of this sequence with themselves.

Crossrefs

Cf. A054390, A237651, A309045, A321344.

Programs

Mathematica

nmax = 52; CoefficientList[Series[Product[(1 + x^(3^k) + x^(2 3^k) + x^(3^(k + 1)))^(3^k), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]
nmax = 52; A[] = 1; Do[A[x] = (1 + x + x^2 + x^3) A[x^3]^3 + 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)))^(3^k).

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