OFFSET
0,16
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
M. D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
a(n) = 1/2*( d_{1, 3}(8n+13) - d_{2, 3}(8n+13) ) where d_{a, m}(n) equals the number of divisors of n which are congruent to a mod m.
Expansion of q^(-13/8)*(eta(q^2)*eta(q^24))^2/(eta(q)*eta(q^12)) in powers of q. - Michael Somos, Sep 29 2006
Expansion of psi(q)*psi(q^12) in powers of q where psi() is a Ramanujan theta function. - Michael Somos, Sep 29 2006
Euler transform of period 24 sequence [ 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -2, ...]. - Michael Somos, Sep 29 2006
a(3n+2)=0. - Michael Somos, Sep 29 2006
EXAMPLE
a(15) = 2 since we can write 15 = 15 + 12*0 = 3 + 12*1.
MATHEMATICA
a[n_] := DivisorSum[8n+13, KroneckerSymbol[-3, #]&]/2; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Dec 04 2015, adapted from PARI *)
PROG
(PARI) {a(n)=if(n<0, 0, n=8*n+13; sumdiv(n, d, kronecker(-3, d))/2)} /* Michael Somos, Sep 29 2006 */
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2*eta(x^24+A)^2/eta(x+A)/eta(x^12+A), n))} /* Michael Somos, Sep 29 2006 */
CROSSREFS
KEYWORD
nonn
AUTHOR
James A. Sellers, Dec 21 2005
STATUS
approved