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 A230205 Expansion of phi(-x) * f(x^1, x^7) in powers of x where phi(), f() are Ramanujan theta functions. 1
 1, -1, -2, 0, 2, 2, 0, 1, -2, -2, -1, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, 1, 0, 0, -2, 2, 1, -2, 0, 0, 0, -2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 1, 0, -2, 0, 0, -2, 0, -1, -2, -2, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, -1, -4, 0, 0 (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). 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 Euler transform of period 16 sequence [ -1, -2, -2, -1, -2, -1, -1, -2, -1, -1, -2, -1, -2, -2, -1, -2, ...]. a(n) = - A030204(2*n + 1). EXAMPLE G.f. = 1 - x - 2*x^2 + 2*x^4 + 2*x^5 + x^7 - 2*x^8 - 2*x^9 - x^10 + ... G.f. = q^9 - q^25 - 2*q^41 + 2*q^73 + 2*q^89 + q^121 - 2*q^137 - 2*q^153 + ... MATHEMATICA a[ n_]:= SeriesCoefficient[EllipticTheta[4, 0, q]*QPochhammer[-q^1, q^8]* QPochhammer[-q^7, q^8]*QPochhammer[q^8], {q, 0, n}]; PROG (PARI) {a(n) = local(m, j); if( n<0, 0, m = 16*n + 9; sum( k=0, sqrtint(m \ 4), if( issquare(m - 16*k^2, &j), if( k==0, 1, 2) * (-1)^k * ((j%8)==3 || (j%8==5)))))} CROSSREFS Cf. A030204. Sequence in context: A307694 A106277 A088627 * A334841 A024713 A361166 Adjacent sequences: A230202 A230203 A230204 * A230206 A230207 A230208 KEYWORD sign AUTHOR Michael Somos, Oct 11 2013 STATUS approved

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Last modified February 25 19:44 EST 2024. Contains 370332 sequences. (Running on oeis4.)