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 A099922 #14 May 25 2019 10:27:17
%S A099922 1,17,138,979,6755,46356,317797,2178293,14930334,102334135,701408711,
%T A099922 4807526952,32951280073,225851433689,1548008755890,10610209857691,
%U A099922 72723460248107,498454011879228,3416454622906669,23416728348467645
%N A099922 a(n) = F(4n) - 2n, where F(n) = Fibonacci numbers A000045.
%D A099922 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 54.
%H A099922 Colin Barker, <a href="/A099922/b099922.txt">Table of n, a(n) for n = 1..1000</a>
%H A099922 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-16,9,-1)
%F A099922 G.f.: x*(1+8*x+x^2)/((1-x)^2 * (1-7*x+x^2)). [Corrected for offset by _Georg Fischer_, May 24 2019]
%F A099922 a(n) = Sum_{k=1..n} Lucas(2k-1)^2.
%F A099922 From _Colin Barker_, May 25 2019: (Start)
%F A099922 a(n) = (-((7-3*sqrt(5))/2)^n + ((7+3*sqrt(5))/2)^n)/sqrt(5) - 2*n.
%F A099922 a(n) = 9*a(n-1) - 16*a(n-2) + 9*a(n-3) - a(n-4) for n>4.
%F A099922 (End)
%t A099922 Rest[CoefficientList[Series[x*(1+8x+x^2)/((1-x)^2*(1-7x+x^2)), {x, 0, 20}], x]] (* _Georg Fischer_, May 24 2019 *)
%o A099922 (PARI) Vec(x*(1 + 8*x + x^2) / ((1 - x)^2*(1 - 7*x + x^2)) + O(x^25)) \\ _Colin Barker_, May 25 2019
%Y A099922 Equals A033888(n) - 2n. Partial sums of A081071. Bisection of A054452.
%K A099922 nonn
%O A099922 1,2
%A A099922 _Ralf Stephan_, Nov 01 2004