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 A208851 Partitions of 2*n + 1 into parts not congruent to 0, +-4, +-6, +-10, 16 (mod 32). 4
 1, 3, 6, 11, 20, 34, 56, 91, 143, 220, 334, 498, 732, 1064, 1528, 2171, 3058, 4269, 5910, 8124, 11088, 15034, 20264, 27154, 36189, 47988, 63324, 83176, 108780, 141672, 183776, 237499, 305812, 392406, 501856, 639781, 813108, 1030354, 1301928, 1640572, 2061850 (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 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of (phi(q^2) / phi(-q) - 1) / (2 * q) in powers of q where phi() is a Ramanujan theta function. Euler transform of period 16 sequence [ 3, 0, 1, 2, 1, 2, 3, 0, 3, 2, 1, 2, 1, 0, 3, 0, ...]. 2 * a(n) = A208850(n + 1). a(n) = A185083(n + 1). EXAMPLE 1 + 3*q + 6*q^2 + 11*q^3 + 20*q^4 + 34*q^5 + 56*q^6 + 91*q^7 + 143*q^8 + ... a(2) = 6 since 2*2 + 1 = 5 = 3 + 2 = 3 + 1 + 1 = 2 + 2 + 1 = 2 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 in 6 ways. MATHEMATICA a[n_]:= SeriesCoefficient[(EllipticTheta[3, 0, q^2]/EllipticTheta[3, 0, -q] - 1)/(2*q), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 05 2018 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, n = 2*n + 2; A = x * O(x^n); polcoeff( (eta(x^2 + A)^3 / (eta(x + A)^2 * eta(x^4 + A)) - 1) / 2, n))} CROSSREFS Cf. A185083, A208850. Sequence in context: A116365 A297443 A185083 * A182845 A265076 A055417 Adjacent sequences: A208848 A208849 A208850 * A208852 A208853 A208854 KEYWORD nonn AUTHOR Michael Somos, Mar 02 2012 STATUS approved

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Last modified December 1 13:31 EST 2023. Contains 367475 sequences. (Running on oeis4.)