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 A363754 #33 Jun 25 2023 03:51:23
%S A363754 0,1,16,276,4917,88132,1581196,28372701,509125596,9135883240,
%T A363754 163936760185,2941725767256,52787126964456,947226559367881,
%U A363754 16997290941068152,305004010378316172,5473074895864584141,98210344115173624636,1762313119177232976916,31623425801074947486405
%N A363754 a(n) = Sum_{k=0..n} F(2k-1)*F(2k)*F(2k+1)/2, where F(n) is the Fibonacci number A000045(n).
%C A363754 This is one of the triple Fibonacci sums that were considered by Subba Rao (1953).
%C A363754 Taking any of the given closed-form expressions for a(n) with Fibonacci numbers, one can extend a(n) to negative indices by using the property F(-n)=(-1)^(n+1). This gives a(-n)=a(n-1).
%H A363754 K. Subba Rao, <a href="https://www.jstor.org/stable/2307147">Some properties of Fibonacci numbers</a>, The American Mathematical Monthly, 60(10):680-684, December 1953.
%H A363754 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (22,-77,77,-22,1).
%F A363754 a(n) = (F(2n+1)^3 + F(2n+1) - 2)/8.
%F A363754 a(n) = (F(6*n+3)+8*F(2*n+1)-10)/40.
%F A363754 a(n) = 22*a(n-1) - 77*a(n-2) + 77*a(n-3) - 22*a(n-4) + a(n-5).
%F A363754 G.f.: x*(1 - 6*x + x^2)/((1 - x)*(1 - 3*x + x^2)*(1 - 18*x + x^2)).
%t A363754 LinearRecurrence[{22, -77, 77, -22, 1}, {0, 1, 16, 276, 4917}]
%Y A363754 Cf. A000045, A256178, A363753.
%K A363754 nonn,easy
%O A363754 0,3
%A A363754 _Hans J. H. Tuenter_, Jun 19 2023