OFFSET
0,2
COMMENTS
Compare the g.f. to the Lambert series of A122859: 1 - 6*Sum_{n>=1} Kronecker(n,3)*x^n/(1+x^n).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
G.f.: A(x) = 1 - 6*x + 24*x^2 - 30*x^3 - 72*x^4 + 840*x^6 - 2028*x^7 + ...
where A(x) = 1 - 1*6*x + 2*12*x^2 - 5*6*x^3 - 12*6*x^4 + 70*12*x^6 - 169*12*x^7 + 408*12*x^8 - 985*6*x^9 + ... + Pell(n)*A122859(n)*x^n + ...
The g.f. is also given by the identity:
A(x) = 1 - 6*( 1*x/(1+2*x-x^2) - 2*x^2/(1+6*x^2+x^4) + 12*x^4/(1+34*x^4+x^8) - 29*x^5/(1+82*x^5-x^10) + 169*x^7/(1+478*x^7-x^14) - 408*x^8/(1+1154*x^8+x^16) + ...).
The values of the symbol Kronecker(n,3) repeat [1,-1,0, ...].
MATHEMATICA
A122859[n_]:= SeriesCoefficient[EllipticTheta[4, 0, q]^3/EllipticTheta[4, 0, q^3], {q, 0, n}]; Join[{1}, Table[Fibonacci[n, 2]*A122859[n], {n, 1, 50}]] (* G. C. Greubel, Jan 02 2017 *)
PROG
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 10 2012
STATUS
approved