This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A259896 Expansion of psi(x) * psi(x^6) in powers of x where phi() is a Ramanujan theta function. 6
 1, 1, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 3, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). Also the number of positive odd solutions to equation x^2 + 6*y^2 = 8*n + 7. - Seiichi Manyama, May 28 2017 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-7/8) * eta(q^2)^2 * eta(q^12)^2 / (eta(q) * eta(q^6)) in powers of q. Euler transform of period 12 sequence [ 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -2, ...]. a(3*n + 1) = A259895(n). a(3*n + 2) = a(9*n + 4) = 0. EXAMPLE G.f. = 1 + x + x^3 + 2*x^6 + x^7 + x^9 + x^10 + x^12 + x^15 + x^16 + ... G.f. = q^7 + q^15 + q^31 + 2*q^55 + q^63 + q^79 + q^87 + q^103 + q^127 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x^(1/2)] EllipticTheta[ 2, 0, x^3] / (4 q^(7/8)), {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^12 + A)^2 / (eta(x + A) * eta(x^6 + A)), n))}; CROSSREFS Cf. A259895. Sequence in context: A045706 A045634 A141702 * A113313 A074871 A182641 Adjacent sequences:  A259893 A259894 A259895 * A259897 A259898 A259899 KEYWORD nonn AUTHOR Michael Somos, Jul 07 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)