OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Michael Somos, Introduction to Ramanujan theta functions, 2019.
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions.
FORMULA
f(x,x^m) = 1 + Sum_{k>=1} x^((m+1)*k*(k-1)/2) (x^k + x^(m*k)). - N. J. A. Sloane, Jan 30 2017
Euler transform of period 18 sequence [1, -1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, -1, 1, -1, ...].
Characteristic function of generalized 11-gonal numbers A195160.
G.f.: Sum_{k in Z} x^(k*(9*k + 7)/2).
G.f.: Product_{k>0} (1 + x^(9*k-8)) * (1 + x^(9*k-1)) * (1 - x^(9*k)).
Sum_{k=1..n} a(k) ~ (2*sqrt(2)/3) * sqrt(n). - Amiram Eldar, Jan 13 2024
EXAMPLE
G.f. = 1 + x + x^8 + x^11 + x^25 + x^30 + x^51 + x^58 + x^86 + x^95 + ...
G.f. = q^49 + q^121 + q^625 + q^841 + q^1849 + q^2209 + q^3721 + q^4225 + ...
MATHEMATICA
a[ n_] := SquaresR[ 1, 72 n + 49] / 2;
a[ n_] := If[ n < 0, 0, Boole @ IntegerQ @ Sqrt @ (72 n + 49)];
a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^9] QPochhammer[ -x^8, x^9] QPochhammer[ x^9], {x, 0, n}];
PROG
(PARI) {a(n) = issquare(72*n + 49)};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 30 2017
STATUS
approved