OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..140
V. Kotesovec, Interesting asymptotic formulas for binomial sums, Jun 09 2013
FORMULA
a(n) = Sum_{k=0..n} Fibonacci(k)^(n-k).
a(n) ~ c * ((1+sqrt(5))/2)^(n^2/4) / 5^(n/4), where c = Sum_{k=-Infinity..Infinity} 5^(k/2)*((1+sqrt(5))/2)^(-k^2) = 3.5769727481316948565395...(see A219781) if n is even and c = Sum_{k=-Infinity..Infinity} 5^((k+1/2)/2)*((1+sqrt(5))/2)^(-(k+1/2)^2) = 3.5769727390073366345992... if n is odd. - Vaclav Kotesovec, Nov 29 2012
EXAMPLE
A(x) = 1 + x/(1-x) + x^2/(1-x) + x^3/(1-2x) + x^4/(1-3x) + x^5/(1-5x) +...
MATHEMATICA
Flatten[{1, Table[Sum[Fibonacci[k]^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Nov 29 2012 *)
PROG
(PARI) a(n)=sum(k=0, n, fibonacci(k)^(n-k))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 09 2007
STATUS
approved