OFFSET
0,3
COMMENTS
The greedy inverse (first occurrence of n) starts 1, 0, 2, 18, 11, 900, 116, 44118, 515, 3105, 5702, ... - R. J. Mathar, Apr 28 2020
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
FORMULA
a(n) = d_{1, 3}(8n+3) - d_{2, 3}(8n+3) where d_{a, m}(n) equals the number of divisors of n which are congruent to a mod m.
Euler transform of period 24 sequence [0, 2, 1, -3, 0, 1, 0, -1, 1, 2, 0, -4, 0, 2, 1, -1, 0, 1, 0, -3, 1, 2, 0, -2, ...]. - Michael Somos, Jan 01 2006
Expansion of q^(-3/8)*(eta(q^4)^5*eta(q^6)^2)/(eta(q^2)^2*eta(q^3)*eta(q^8)^2) in powers of q.
a(n) = A002324(8*n+3).
EXAMPLE
a(11) = 4 since we can write 11 = 2*(2)^2 + 3*1 = 2*(-2)^2 + 3*1 = 2*(1)^2 + 3*3 = 2*(-1)^2 + 3*3
MATHEMATICA
eta[x_] := x^(1/24)*QPochhammer[x]; A112608[n_] := SeriesCoefficient[ q^(-3/8)*(eta[q^4]^5*eta[q^6]^2)/(eta[q^2]^2*eta[q^3]*eta[q^8]^2), {q, 0, n}]; Table[A112608[n], {n, 0, 50}] (* G. C. Greubel, Sep 25 2017 *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)^5*eta(x^6+A)^2/ eta(x^2+A)^2/eta(x^3+A)/eta(x^8)^2, n))} /* Michael Somos, Jan 01 2006 */
CROSSREFS
KEYWORD
nonn
AUTHOR
James A. Sellers, Dec 21 2005
STATUS
approved