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A208546
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.
2
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
OFFSET
0,1
LINKS
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/4) * x^(3*k * (5*k + 1)/2) * (x^(4*k + 1) + x^(-16*k + 7)).
EXAMPLE
G.f. = 1 + x - x^3 + x^7 + x^8 + x^14 - x^20 - x^29 + x^31 + x^42 - x^52 - x^66 + ...
G.f. = q + q^121 - q^361 + q^841 + q^961 + q^1681 - q^2401 - q^3481 + q^3721 + ...
MATHEMATICA
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; CoefficientList[Series[f[-x^29, x^31] + x*f[-x^19, x^41] - x^3*f[-x^11, x^49] + x^7*f[x, -x^59], {x, 0, 50}], x] (* G. C. Greubel, Aug 11 2018 *)
PROG
(PARI) {a(n) = local(m); if( issquare( 120*n + 1, &m), (-1)^(m \ 40 + m \ 12))}
CROSSREFS
Sequence in context: A359818 A207710 A207735 * A113430 A214529 A113681
KEYWORD
sign
AUTHOR
Michael Somos, Feb 28 2012
STATUS
approved