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

%I

%S 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,

%T 38,110,72,72,158,86,86,190,104,104,289,185,185,395,210,210,455,245,

%U 245,645,400,400,829,429,429,915,486,486,1269,783,783,1623,840,840,1800,960,960,2472

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

%C The trisection equals the self-convolution of this sequence.

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

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

%t 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]

%t 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]

%Y Cf. A054390, A237651, A309046.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jul 09 2019

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Last modified October 21 04:00 EDT 2021. Contains 348141 sequences. (Running on oeis4.)