OFFSET
0,1
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Michael Somos, Introduction to Ramanujan theta functions, 2019.
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions.
FORMULA
Euler transform of period 16 sequence [ 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, -1, 1, -1, ...].
G.f.: f(x, x^7) = sum_{k in Z} x^(4*k^2 - 3*k).
Sum_{k=1..n} a(k) ~ sqrt(n). - Amiram Eldar, Jan 13 2024
EXAMPLE
G.f. = 1 + x + x^7 + x^10 + x^22 + x^27 + x^45 + x^52 + x^76 + x^85 + x^115 + ...
G.f. = q^9 + q^25 + q^121 + q^169 + q^361 + q^441 + q^729 + q^841 + q^1225 + ...
MATHEMATICA
f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; Table[SeriesCoefficient[f[q, q^7], {q, 0, n}], {n, 0, 50}] (* G. C. Greubel, Oct 05 2017 *)
PROG
(PARI) {a(n) = issquare(16*n + 9)};
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos and Omar E. Pol, Jul 09 2012
STATUS
approved