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 A214505 a(n) = 1 if n is four times a triangular number, -1 if one more than twelve times a triangular number else 0. 2
 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 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, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (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). LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 S. Cooper and M. Hirschhorn, On some infinite product identities, Rocky Mountain J. Math., 31 (2001) 131-139. see p. 134 Theorem 5. Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of psi(x^4) - x * psi(x^12) in powers of x where psi() is a Ramanujan theta function. Expansion of f(-x, x^5) * f(-x^4, -x^8) / f(x, -x) in powers of x where f(,) is the Ramanujan two-variable theta function. Euler transform of period 24 sequence [ -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, ...]. G.f.: (Sum_{k} x^(2*k*(k + 1)) - x^(6*k*(k + 1) + 1)) / 2. a(n) = A214295(2*n + 1). EXAMPLE 1 - x + x^4 + x^12 - x^13 + x^24 - x^37 + x^40 + x^60 - x^73 + x^84 + ... q - q^3 + q^9 + q^25 - q^27 + q^49 - q^75 + q^81 + q^121 - q^147 + q^169 + ... PROG (PARI) {a(n) = n = 2*n + 1; issquare(n) - issquare(3*n)} CROSSREFS Cf. A010052, A214295. Sequence in context: A016039 A138149 A113047 * A127692 A014305 A023533 Adjacent sequences:  A214502 A214503 A214504 * A214506 A214507 A214508 KEYWORD sign AUTHOR Michael Somos, Jul 19 2012 STATUS approved

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Last modified April 3 20:26 EDT 2020. Contains 333199 sequences. (Running on oeis4.)