OFFSET
1,8
COMMENTS
FORMULA
G.f.: Sum_{n>=1} A210826(n)*Fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) = Sum_{n>=1} Fibonacci(n^3)*x^(n^3).
EXAMPLE
G.f.: A(x) = x + 21*x^8 + 196418*x^27 + 10610209857723*x^64 + 59425114757512643212875125*x^125 +...
where A(x) = x/(1-x-x^2) + (-1)*1*x^2/(1-3*x^2+x^4) + (-1)*2*x^3/(1-4*x^3-x^6) + (0)*3*x^4/(1-7*x^4+x^8) + (-1)*5*x^5/(1-11*x^5-x^10) + (+1)*8*x^6/(1-18*x^6+x^12)+ (-1)*13*x^7/(1-29*x^7-x^14) + (+1)*21*x^8/(1-47*x^8+x^16) + (0)*34*x^9/(1-76*x^9-x^18) + (+1)*55*x^10/(1-123*x^10+x^20)+ (-1)*89*x^11/(1-199*x^11-x^22) +...+ A210826(n)*Fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) +...
The sequence A210826(n) = kronecker(-3, d(n)) begins:
[1,-1,-1,0,-1,1,-1,1,0,1,-1,0,-1,1,1,-1,-1,0,-1,0,1,1,-1,-1,0,1,1,...].
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 07 2012
STATUS
approved