0,10

I. J. Zucker, "Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums." J. Phys. A: Math. Gen. 23, 117-132, 1990.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

a(n)=-b(n) where b(n) is multiplicative and b(3^e) = -2(1+(-1)^e)/2 if e>0, b(p^e) = (1+(-1)^e)/2 otherwise.

Expansion of Jacobi theta function theta_3(Pi/3, q) in powers of q. - Michael Somos, Jan 26, 2006

Expansion of eta(q)eta(q^4)eta(q^6)^2/(eta(q^2)eta(q^3)eta(q^12)) in powers of q. - Michael Somos Nov 05 2005

Euler transform of period 12 sequence [ -1, 0, 0, -1, -1, -1, -1, -1, 0, 0, -1, -1, ...]. - Michael Somos Nov 05 2005

G.f.: (Sum_{k} 3x^((3k)^2) - x^(k^2))/2 = Product_{k>0} (1-x^k)/((1-x^(12k-2))(1-x^(12k-3))(1-x^(12k-9))(1-x^(12k-10))) - Michael Somos Nov 05 2005

Expansion of chi(q^3) * psi(-q) in powers of q where chi(), psi() are Ramanujan theta functions. - Michael Somos May 19 2007

G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 18^(1/2) (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A089801.

Expansion of f(x*w, x/w) in powers of x where w is a primitive cube root of unity and f() is Ramanujan's two variable theta function. - Michael Somos Sep 17 2007

1 - q - q^4 + 2*q^9 - q^16 - q^25 + 2*q^36 - q^49 - q^64 + 2*q^81 + ...

(PARI) a(n)=if(n<1, n==0, issquare(n)*(3*(n%3==0)-1)) /* Michael Somos Nov 05 2005 */

Sequence in context: A002483 A060478 A088806 this_sequence A089810 A096562 A096563

Adjacent sequences: A089804 A089805 A089806 this_sequence A089808 A089809 A089810

sign

Eric Weisstein (eric(AT)weisstein.com), Nov 12, 2003