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a(n) = Fibonacci(n)*A008655(n) for n>= >= 1, with a(0)=1, where A008655 lists the coefficients in (theta_3(x)*theta_3(3*x)+) + theta_2(x)*theta_2(3*x))^4.

G.f.: A(x) = 1 + 24*x + 216*x^2 + 1776*x^3 + 5256*x^4 + 15120*x^5 +... + ...

where A(x) = 1 + 1*24*x + 1*216*x^2 + 2*888*x^3 + 3*1752*x^4 + 5*3024*x^5 +...+ + ... + Fibonacci(n)*A008655(n)*x^n +... + ...

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G. C. Greubel, <a href="/A205968/b205968.txt">Table of n, a(n) for n = 0..1000</a>

A008655 := CoefficientList[Series[((EllipticTheta[3, 0, q]^3 + EllipticTheta[3, Pi/3, q]^3 + EllipticTheta[3, 2 Pi/3, q]^3)^4/(3* EllipticTheta[3, 0, q^3])^4), {q, 0, 250}], q]; b := Table[A008655[[n]], {n, 1, 120}][[1 ;; ;; 2]]; Join[{1}, Table[Fibonacci[n]*b[[n + 1]], {n, 1, 50}]] (* G. C. Greubel, Jul 16 2018 *)

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_Paul D. Hanna (pauldhanna(AT)juno.com), _, Feb 04 2012

OEIS Server: https://oeis.org/edit/global/213

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Cf. A209448 (Pell variant).

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