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A232635 Expansion of psi(x) * phi(x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions. 1
1, 1, 4, 5, 4, 8, 1, 4, 8, 4, 13, 12, 4, 8, 8, 1, 12, 8, 8, 12, 16, 13, 4, 16, 4, 12, 20, 8, 5, 12, 12, 12, 16, 8, 8, 20, 17, 16, 16, 8, 20, 24, 8, 8, 16, 1, 24, 16, 8, 12, 20, 16, 12, 28, 12, 33, 20, 8, 16, 12, 16, 20, 24, 8, 16, 32, 1, 12, 32, 8, 16, 32, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Theta function of cubic lattice with respect to point (1/4, 0, 0).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-1/8) * eta(q^4)^10 / (eta(q) * eta(q^2)^2 * eta(q^8)^4) in powers of q.

Euler transform of period 8 sequence [ 1, 3, 1, -7, 1, 3, 1, -3, ...].

a(3*n + 2) = 4 * A213023(n).

EXAMPLE

G.f. = 1 + x + 4*x^2 + 5*x^3 + 4*x^4 + 8*x^5 + x^6 + 4*x^7 + 8*x^8 + 4*x^9 + ...

G.f. = q + q^9 + 4*q^17 + 5*q^25 + 4*q^33 + 8*q^41 + q^49 + 4*q^57 + 8*q^65 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ q^4]^10 / (QPochhammer[ q] QPochhammer[ q^2]^2 QPochhammer[ q^8]^4), {q, 0, n}]

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^10 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^4), n))}

CROSSREFS

Cf. A213023.

Sequence in context: A278713 A200623 A248671 * A201296 A246954 A045834

Adjacent sequences:  A232632 A232633 A232634 * A232636 A232637 A232638

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 27 2013

STATUS

approved

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Last modified January 25 23:08 EST 2020. Contains 331270 sequences. (Running on oeis4.)