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 A215040 #19 Jan 05 2025 19:51:39
%S A215040 1,8,125,2197,39304,704969,12649337,226981000,4073003173,73087061741,
%T A215040 1311494070536,23533806109393,422297015640625,7577812474746632,
%U A215040 135978327528030989,2440032083025183109,43784599166913148552,785682752921379769625,14098504953417839657513
%N A215040 a(n) = F(2*n+1)^3, n>=0, with F = A000045 (Fibonacci).
%C A215040 Bisection (odd part) of A056570. From this follows the o.g.f., and its partial fraction decomposition leads to the explicit formula given below. For the computation see A215039 for a comment on Chebyshev's S-polynomials.
%H A215040 Harvey P. Dale, <a href="/A215040/b215040.txt">Table of n, a(n) for n = 0..797</a>
%H A215040 Kenny B. Davenport, proposer, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/FQElemProbAug2024.pdf">Problem B-1353</a>, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 62, No. 3 (2024), p. 259.
%F A215040 a(n) = F(2*n+1)^3, n>=0, with F=A000045.
%F A215040 O.g.f.: (1-x)*(1-12*x+x^2)/((1-3*x+x^2)*(1-18*x+x^2)) (from the bisection (odd part) of A056570).
%F A215040 a(n) = (12*F(2*n+1) + F(6*(n+1)) - F(6*n))/20, n>=0.
%F A215040 a(n) = 1 + (4*Sum_{k=1..n} F(6*k) + 3*Sum_{k=1..n} F(2*k)) / 5 (Davenport, 2024). - _Amiram Eldar_, Aug 29 2024
%t A215040 Fibonacci[2*Range[0,20]+1]^3 (* _Harvey P. Dale_, Jan 24 2013 *)
%Y A215040 Cf. A000045, A056570, A163200 (partial sums).
%K A215040 nonn,easy
%O A215040 0,2
%A A215040 _Wolfdieter Lang_, Aug 10 2012