A113122 a(n) = Sum_{i=1..n} F(i)^F(n-i+1).

1, 2, 4, 7, 14, 32, 107, 724, 18616, 4117597, 28878084584, 53183366452504936, 794001316484619940422835765, 25210343943654420841949267608211227900299990, 14311021641196256564899251685012421154803682074917148917844556724305980

Offset: 1

Author

Jonathan Vos Post, Jan 04 2006

Keywords

• easy
• nonn

Examples

			a(1) = F(1)^F(1) = 1^1 = 1.
a(2) = F(1)^F(2) + F(2)^F(1) = 1^1 + 1^1 = 2.
a(3) = F(1)^F(3) + F(2)^F(2) + F(3)^F(1) = 1^2 + 1^1 + 2^1 = 4.
a(4) = F(1)^F(4) + F(2)^F(3) + F(3)^F(2) + F(4)^F(1) = 1^3 + 1^2 + 2^1 + 3^1 = 7.
a(5) = 1^5 + 1^3 + 2^2 + 3^1 + 5^1 = 14.
		

Crossrefs

Cf. A000045.

Programs

Maple

F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= n-> add(F(i)^F(n-i+1), i=1..n):
seq(a(n), n=1..16);  # Alois P. Heinz, Aug 09 2018

Mathematica

Table[Sum[(Fibonacci[k])^(Fibonacci[n - k + 1]), {k, 1, n}], {n, 1, 15}] (* G. C. Greubel, May 18 2017 *)

PARI

a(n)=sum(k=1,n, (fibonacci(k))^(fibonacci(n-k+1))) \\ G. C. Greubel, May 18 2017

Formula

a(n) = Sum_{i=1..n} F(i)^F(n-i+1).

a(n) ~ 2^(phi^(n-2)/sqrt(5)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Jun 07 2025