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 A127595 #25 Jan 05 2023 19:08:40
%S A127595 0,1,15,128,945,6655,46080,317057,2176335,14925184,102320625,
%T A127595 701373311,4807434240,32951037313,225850798095,1548007091840,
%U A127595 10610205501105,72723448842367,498453982018560,3416454544730369,23416728143799375
%N A127595 a(n) = F(4n) - 2F(2n) where F(n) = Fibonacci numbers A000045.
%C A127595 a(n) is a divisibility sequence; that is, if h|k then a(h)|a(k).
%H A127595 Michael De Vlieger, <a href="/A127595/b127595.txt">Table of n, a(n) for n = 0..1196</a>
%H A127595 E. L. Roettger and H. C. Williams, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Roettger/roettger12.html">Appearance of Primes in Fourth-Order Odd Divisibility Sequences</a>, J. Int. Seq., Vol. 24 (2021), Article 21.7.5.
%H A127595 Hugh Williams and R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277.
%H A127595 H. C. Williams and R. K. Guy, <a href="http://www.emis.de/journals/INTEGERS/papers/p33/p33.Abstract.html">Odd and even linear divisibility sequences of order 4</a>, INTEGERS, 2015, #A33.
%H A127595 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A127595 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23,10,-1).
%F A127595 a(n) = F(2n)*(L(2n)-2) = A001906(n)*A004146(n), where L(n) are the Lucas numbers A000032.
%F A127595 a(2n) = 5*(F(2n))^3*L(2n), a(2n+1) = F(2n+1)*L(2n+1)^3.
%F A127595 a(n) = [(Phi^(2n))-1]^2*[(Phi^(4n))-1]/[sqrt(5)*(Phi^(4n))].
%F A127595 G.f.: A(x)=x*(1+(r+2)*x+x^2)/((1-r*x+x^2)*(1-(r^2-2)*x+x^2)) at r=3. The case r=2 is A000578.
%F A127595 a(n) = -a(-n) for all n in Z. - _Michael Somos_, Dec 30 2022
%e A127595 G.f. = x + 15*x^2 + 128*x^3 + 945*x^4 + 6655*x^5 + ... - _Michael Somos_, Dec 30 2022
%t A127595 With[{r = 3}, CoefficientList[Series[x (1 + (r + 2) x + x^2)/((1 - r x + x^2)*(1 - (r^2 - 2)*x + x^2)), {x, 0, 20}], x]] (* _Michael De Vlieger_, Nov 09 2021 *)
%o A127595 (PARI) {a(n) = my(w = quadgen(5)^(2*n)); imag(w^2 - 2*w)}; /* _Michael Somos_, Dec 30 2022 */
%Y A127595 Cf. A000032, A000045, A001906, A004146.
%K A127595 easy,nonn
%O A127595 0,3
%A A127595 _Peter Bala_, Apr 10 2007