OFFSET
1,2
COMMENTS
FORMULA
a(n) = Lucas(n)^2 for odd n, a(n) = Lucas(n)^2 - 2 for even n>0.
O.g.f.: x*(1+4*x-5*x^2+2*x^3)/((1-x^2)*(1-3*x+x^2)).
EXAMPLE
G.f.: L(x) = x + 7*x^2/2 + 16*x^3/3 + 47*x^4/4 + 121*x^5/5 +...
exp(L(x)) = 1 + x + 2^2*x^2 + 3^2*x^3 + 5^2*x^4 + 8^2*x^5 +...
PROG
(PARI) {a(n)=(fibonacci(n-1)+fibonacci(n+1))^2-2*((n-1)%2)}
(PARI) {a(n)=polcoeff(deriv(log(sum(m=0, n, fibonacci(m)^2*x^m)+x*O(x^n))), n)}
(PARI) {a(n)=polcoeff(x*(1+4*x-5*x^2+2*x^3)/((1-x^2)*(1-3*x+x^2+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 24 2010
STATUS
approved