This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113122 #23 Jun 07 2025 11:57:44
%S A113122 1,2,4,7,14,32,107,724,18616,4117597,28878084584,53183366452504936,
%T A113122 794001316484619940422835765,
%U A113122 25210343943654420841949267608211227900299990,14311021641196256564899251685012421154803682074917148917844556724305980
%N A113122 a(n) = Sum_{i=1..n} F(i)^F(n-i+1).
%F A113122 a(n) = Sum_{i=1..n} F(i)^F(n-i+1).
%F A113122 a(n) ~ 2^(phi^(n-2)/sqrt(5)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Jun 07 2025
%e A113122 a(1) = F(1)^F(1) = 1^1 = 1.
%e A113122 a(2) = F(1)^F(2) + F(2)^F(1) = 1^1 + 1^1 = 2.
%e A113122 a(3) = F(1)^F(3) + F(2)^F(2) + F(3)^F(1) = 1^2 + 1^1 + 2^1 = 4.
%e A113122 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.
%e A113122 a(5) = 1^5 + 1^3 + 2^2 + 3^1 + 5^1 = 14.
%p A113122 F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
%p A113122 a:= n-> add(F(i)^F(n-i+1), i=1..n):
%p A113122 seq(a(n), n=1..16); # _Alois P. Heinz_, Aug 09 2018
%t A113122 Table[Sum[(Fibonacci[k])^(Fibonacci[n - k + 1]), {k, 1, n}], {n, 1, 15}] (* _G. C. Greubel_, May 18 2017 *)
%o A113122 (PARI) a(n)=sum(k=1,n, (fibonacci(k))^(fibonacci(n-k+1))) \\ _G. C. Greubel_, May 18 2017
%Y A113122 Cf. A000045.
%K A113122 easy,nonn
%O A113122 1,2
%A A113122 _Jonathan Vos Post_, Jan 04 2006