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A213056
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Expansion of chi(x) * f(x^3)^3 in powers of x where chi(), f() are Ramanujan theta functions.
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2
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1, 1, 0, 4, 4, 1, 4, 4, 5, 0, 0, 8, 4, 4, 4, 8, 9, 4, 0, 4, 12, 1, 4, 8, 8, 4, 0, 8, 8, 4, 8, 16, 8, 5, 0, 12, 12, 0, 8, 12, 13, 0, 0, 8, 8, 8, 12, 8, 16, 4, 0, 16, 12, 4, 4, 20, 13, 4, 0, 16, 20, 8, 8, 8, 8, 9, 0, 12, 16, 4, 12, 12, 16, 0, 0, 16, 20, 4, 8
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OFFSET
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0,4
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COMMENTS
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Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
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LINKS
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Table of n, a(n) for n=0..78.
M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
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Expansion of q^(-1/3) * eta(q^2)^2 * eta(q^6)^9 / (eta(q) * eta(q^3)^3 * eta(q^4) * eta(q^12)^3) in powers of q.
Expansion of q^(-1/9) times theta series of cubic lattice with respect to point [0, 0, 1/3] in powers of q^(1/3).
Euler transform of period 12 sequence [ 1, -1, 4, 0, 1, -7, 1, 0, 4, -1, 1, -3, ...].
G.f.: Product_{k>0} (1 - (-x)^(3*k))^3 * (1 + x^(2*k-1)).
a(4*n + 1) = a(n). a(8*n + 2) = 0.
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EXAMPLE
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1 + x + 4*x^3 + 4*x^4 + x^5 + 4*x^6 + 4*x^7 + 5*x^8 + 8*x^11 + 4*x^12 + ...
q + q^4 + 4*q^10 + 4*q^13 + q^16 + 4*q^19 + 4*q^22 + 5*q^25 + 8*q^34 + ...
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^6 + A)^9 / (eta(x + A) * eta(x^3 + A)^3 * eta(x^4 + A) * eta(x^12 + A)^3) , n))}
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CROSSREFS
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Sequence in context: A030788 A087709 A106642 * A135012 A156380 A166237
Adjacent sequences: A213053 A213054 A213055 * A213057 A213058 A213059
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jun 03 2012
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STATUS
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approved
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