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A129438 Expansion of (phi(q) * phi(q^2) + phi(-q^2) * phi(q^4)) / 2 in powers of q where phi() is a Ramanujan theta function. 1
1, 1, 0, 2, 2, 0, 0, 0, 2, 3, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 1, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, 1, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 6, 2, 0, 2, 4, 0, 0, 0, 0, 5, 0, 2, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Moebius transform is period 32 sequence [1, -1, 1, 2, -1, -1, -1, 0, 1, 1, 1, 2, -1, 1, -1, 0, 1, -1, 1, -2, -1, -1, -1, 0, 1, 1, 1, -2, -1, 1, -1, 0, ...].

a(4*n + 2) = a(8*n + 5) = a(8*n + 7) = 0.

a(n) = A125096(n) unless n=0. a(8*n + 1) = A112603(n). a(8*n + 3) = 2 * A033761(n).

a(2*n + 1) = A113411(n). a(4*n) = A033715(n). - Michael Somos, Nov 11 2015

EXAMPLE

G.f. = 1 + q + 2*q^3 + 2*q^4 + 2*q^8 + 3*q^9 + 2*q^11 + 4*q^12 + 2*q^16 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^2] + EllipticTheta[ 4, 0, q^2] EllipticTheta[ 3, 0, q^4]) / 2, {q, 0, n}]; (* Michael Somos, Nov 11 2015 *)

PROG

(PARI) {a(n) = if( n<1, n==0, qfrep([1, 0; 0, 8], n)[n] + qfrep([3, 1; 1, 3], n)[n])};

CROSSREFS

Cf. A033715, A033761, A112603, A113411, A125096.

Sequence in context: A177338 A024158 A054978 * A125096 A037862 A337113

Adjacent sequences:  A129435 A129436 A129437 * A129439 A129440 A129441

KEYWORD

nonn

AUTHOR

Michael Somos, Apr 14 2007

STATUS

approved

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Last modified July 1 15:38 EDT 2022. Contains 354973 sequences. (Running on oeis4.)