OFFSET
0,1
COMMENTS
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
|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
KEYWORD
sign
AUTHOR
Michael Somos, Jul 20 2012
STATUS
approved