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 A246862 Expansion of phi(x) * f(x^3, x^5) in powers of x where phi(), f() are Ramanujan theta functions. 3
 1, 2, 0, 1, 4, 1, 2, 2, 0, 4, 0, 0, 2, 0, 3, 2, 2, 0, 3, 4, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 4, 0, 0, 1, 4, 0, 2, 2, 0, 5, 2, 2, 2, 4, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 4, 2, 0, 0, 2, 0, 1, 2, 0, 2, 6, 0, 0, 4, 1, 8, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 4, 0, 4, 2, 2 (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 G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Euler transform of period 16 sequence [ 2, -3, 3, -1, 3, -4, 2, -2, 2, -4, 3, -1, 3, -3, 2, -2, ...]. Convolution of A000122 and A214264. a(9*n + 2) = a(9*n + 8) = 0. a(9*n + 5) = A246863(n). a(n) = A113407(2*n) = A226192(2*n) = A008441(4*n) = A134343(4*n) = A116604(8*n) = A125079(8*n) = A129447(8*n) = A138741(8*n). EXAMPLE G.f. = 1 + 2*x + x^3 + 4*x^4 + x^5 + 2*x^6 + 2*x^7 + 4*x^9 + 2*x^12 + ... G.f. = q + 2*q^17 + q^49 + 4*q^65 + q^81 + 2*q^97 + 2*q^113 + 4*q^145 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x] QPochhammer[ -x^3, x^8] QPochhammer[ -x^5, x^8] QPochhammer[ x^8], {x, 0, n}]; PROG (PARI) {a(n) = if( n<0, 0, issquare(16 * n + 1) + 2 * sum(i=1, sqrtint(n), issquare(16 * (n - i^2) + 1)))}; CROSSREFS Cf. A000122, A008441, A113407, A116604, A125079, A129447, A134343, A138741, A214264, A226192, A246863. Sequence in context: A258123 A121583 A228924 * A194686 A302996 A266213 Adjacent sequences:  A246859 A246860 A246861 * A246863 A246864 A246865 KEYWORD nonn AUTHOR Michael Somos, Sep 05 2014 STATUS approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)