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 A185124 Expansion of f(x, -x^5) in powers of x where f(,) is the Ramanujan general theta function. 2
 1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). a(n) is nonzero if and only if n is a number of A001082. The exponents in the q-series for this sequence are the squares of the numbers of A001651. 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 24 sequence [ 1, -1, 0, 0, -1, 1, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, -1, 1, -1, 0, 0, -1, 1, -1, ...]. G.f.: Sum_{k in Z} (-1)^floor(k + 1)/2) * x^(k * (3*k + 2)). a(4*n + 2) = a(4*n + 3) = a(5*n + 2) = a(5*n + 4) = a(8*n + 4) = 0. a(4*n + 1) = A080902(n). a(8*n) = A010815(n). a(n) = (-1)^n * A185125(n). - Michael Somos, Jun 30 2015 EXAMPLE G.f. = 1 + x - x^5 - x^8 - x^16 - x^21 + x^33 + x^40 + x^56 + x^65 - x^85 + ... G.f. = q + q^4 - q^16 - q^25 - q^49 - q^64 + q^100 + q^121 + q^169 + q^196 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x, -x^6] QPochhammer[ x^5, -x^6] QPochhammer[ -x^6], {x, 0, n}]; (* Michael Somos, Jun 30 2015 *) PROG (PARI) {a(n) = my(m); if( issquare( 3*n + 1, &m), (m%3!=0) * (-1)^((m+3) \ 6), 0)}; CROSSREFS Cf. A010815, A080902, A185125. Sequence in context: A089801 A290739 A143064 * A185125 A327580 A163811 Adjacent sequences:  A185121 A185122 A185123 * A185125 A185126 A185127 KEYWORD sign AUTHOR Michael Somos, Jan 20 2012 STATUS approved

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Last modified February 27 13:18 EST 2020. Contains 332306 sequences. (Running on oeis4.)