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 A214529 Expansion of f(x^29, -x^31) - x * f(x^19, -x^41) + x^3 * f(x^11, -x^49) - x^7 * f(-x, x^59) in powers of x where f() is Ramanujan's two-variable theta function. 1
 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 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 (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 G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA |a(n)| is the characteristic function of A093722. The exponents in the q-series q * A(q^120) are the squares of the numbers in A057538. Euler transform of a period 80 sequence. G.f.: Sum_{k} (-1)^(floor((k - 1)/2) + floor(k/4)) * x^(3*k * (5*k + 1)/2) * (x^(4*k + 1) + x^(-16*k + 7)). a(n) = (-1)^n * A208546(n). EXAMPLE 1 - x + x^3 - x^7 + x^8 + x^14 - x^20 + x^29 - x^31 + x^42 - x^52 - x^66 + ... q - q^121 + q^361 - q^841 + q^961 + q^1681 - q^2401 + q^3481 - q^3721 + ... MATHEMATICA a[ n_] := Module[ {m}, If[ n >= 0 && OddQ[ DivisorSigma[ 0, 120 n + 1]], m = Sqrt[ 120 n + 1]; (-1)^(Quotient[ m, 40] + Quotient[ m, 3]), 0]]; Table[a[n], {n, 0, 30}] PROG (PARI) {a(n) = local(m); if( issquare( 120*n + 1, &m), (-1)^(m \ 40 + m \ 3))} CROSSREFS Cf. A057538, A093722, A208546. Sequence in context: A207735 A208546 A113430 * A113681 A295895 A179416 Adjacent sequences:  A214526 A214527 A214528 * A214530 A214531 A214532 KEYWORD sign AUTHOR Michael Somos, Jul 20 2012 STATUS approved

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Last modified August 21 05:30 EDT 2019. Contains 326162 sequences. (Running on oeis4.)