0,31

M. D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211.

a(n) = 1/2*( d_{1, 3}(8n+7) - d_{2, 3}(8n+7) ) where d_{a, m}(n) equals the number of divisors of n which are congruent to a mod m.

Expansion of phi(q^3) * psi(q^4) in powers of q where psi() is a Ramanujan theta function. - Michael Somos Mar 10 2008

Expansion of q^(-7/8) * (eta(q^6) * eta(q^8))^2 / (eta(q^3) * eta(q^4)) in powers of q. - Michael Somos Mar 10 2008

Euler transform of period 24 sequence [ 0, 0, 1, 1, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1, 1, 0, 0, -2, ...]. - Michael Somos Mar 10 2008

G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 3^(1/2) (t/i) g(t) where q = exp(2 pi i t) and g() is g.f. for A138270.

a(3*n+2) = 0.

a(30) = 2 since we can write 30 = 3*10 + 4*0 = 3*6 + 4*3

q^7 + q^31 + q^39 + q^63 + q^79 + q^103 + q^111 + q^127 + q^151 + ...

(PARI) {a(n) = if( n<0, 0, n=8*n+7; sumdiv(n, d, kronecker(-3, d))/2)} /* Michael Somos Mar 10 2008 */

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^8 + A))^2 / (eta(x^3 + A) * eta(x^4 + A)), n))} /* Michael Somos Mar 10 2008 */

A131962(n) = a(3*n). A112607(n) = a(3*n+1). A128617(n) = a(4*n+3).

A112605(2*n+1) = 2 * a(n). A112607(3*n+1) = a(n). A033762(4*n+3) = 2 * a(n). A112604(6*n+5) = 2 * a(n). A002324(8*n+7) = a(n). A123484(24*n+21) = 2 * a(n).

Sequence in context: A109502 A112983 A158785 this_sequence A134363 A054015 A056137

Adjacent sequences: A112606 A112607 A112608 this_sequence A112610 A112611 A112612

nonn

James A. Sellers (sellersj(AT)math.psu.edu), Dec 21 2005