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%I #5 Jul 09 2019 11:24:47
%S 1,1,1,4,3,3,9,6,6,25,19,19,58,39,39,105,66,66,211,145,145,394,249,
%T 249,630,381,381,1114,733,733,1903,1170,1170,2889,1719,1719,4827,3108,
%U 3108,7869,4761,4761,11574,6813,6813,18489,11676,11676,28839,17163,17163,41013,23850
%N Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) + x^(3^(k+1)))^(3^k).
%C The trisection equals the three-fold convolution of this sequence with themselves.
%F G.f.: Product_{k>=0} ((1 - x^(4*3^k))/(1 - x^(3^k)))^(3^k).
%F G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3) * A(x^3)^3.
%t 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]
%t 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]
%Y Cf. A054390, A237651, A309045, A321344.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Jul 09 2019
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