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A230204 Expansion of phi(-x) * f(x^3, x^5) in powers of x where phi(), f() are Ramanujan theta functions. 2
1, -2, 0, 1, 0, 1, -2, 2, 0, 0, 0, 0, -2, 0, -1, -2, 2, 0, 3, 0, 0, 2, 2, -2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, -2, 2, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, 2, 0, 0, -2, 0, 1, -2, 0, -2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, -2, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 16 sequence [ -2, -1, -1, -1, -1, -2, -2, -2, -2, -2, -1, -1, -1, -1, -2, -2, ...].
a(n) = A030204(2*n).
EXAMPLE
G.f. = 1 - 2*x + x^3 + x^5 - 2*x^6 + 2*x^7 - 2*x^12 - x^14 - 2*x^15 + ...
G.f. = q - 2*q^17 + q^49 + q^81 - 2*q^97 + 2*q^113 - 2*q^193 - q^225 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q] QPochhammer[ -q^3, q^8] QPochhammer[ -q^5, q^8] QPochhammer[ q^8], {q, 0, n}];
PROG
(PARI) {a(n) = local(m, j); if( n<0, 0, m = 16*n + 1; sum( k=0, sqrtint(m \ 4), if( issquare(m - 16*k^2, &j), if( k==0, 1, 2) * (-1)^k * ((j%8)==1 || (j%8==7)))))}
CROSSREFS
Cf. A030204.
Sequence in context: A090239 A165276 A035698 * A325592 A161502 A279628
KEYWORD
sign
AUTHOR
Michael Somos, Oct 11 2013
STATUS
approved

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Last modified March 2 15:45 EST 2024. Contains 370494 sequences. (Running on oeis4.)