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 A157459 #33 Dec 03 2024 08:26:23
%S A157459 0,72,23256,7488432,2411251920,776415629880,250003421569512,
%T A157459 80500325329753056,25920854752758914592,8346434730063040745640,
%U A157459 2687526062225546361181560,865375045601895865259716752,278648077157748243067267612656,89723815469749332371794911558552
%N A157459 Expansion of 72*x^2 / (1 - 323*x + 323*x^2 - x^3).
%C A157459 This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
%C A157459 A * c(n) + 1 = a(n)^2,
%C A157459 (A+1) * c(n) + 1 = b(n)^2; for details see comment in A157014.
%C A157459 A157459 is the c(n) sequence for A=4.
%H A157459 Colin Barker, <a href="/A157459/b157459.txt">Table of n, a(n) for n = 1..250</a>
%H A157459 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (323,-323,1).
%F A157459 4*a(n) + 1 = A007805(n-1)^2.
%F A157459 5*a(n) + 1 = A049629(n-1)^2.
%F A157459 G.f.: 72*x^2/(1 - 323*x + 323*x^2 - x^3).
%F A157459 c(1) = 0, c(2) = 72, c(3) = 323*c(2), c(n) = 323*(c(n-1) - c(n-2)) + c(n-3) for n>3.
%F A157459 a(n) = -((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)*(9+4*sqrt(5)+(-9+4*sqrt(5))*(161+72*sqrt(5))^n))/80. - _Colin Barker_, Jul 25 2016
%F A157459 a(n) = 72*A298271(n-1). - _Greg Dresden_, Dec 02 2021
%F A157459 a(n) = 2*A201003(n-1). - _Amiram Eldar_, Dec 01 2024
%t A157459 LinearRecurrence[{323,-323,1},{0,72,23256},20] (* _Harvey P. Dale_, Feb 28 2021 *)
%o A157459 (PARI) concat(0, Vec(72*x^2/(1-323*x+323*x^2-x^3)+O(x^20))) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A157459 (PARI) a(n) = -round((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)*(9+4*sqrt(5)+(-9+4*sqrt(5))*(161+72*sqrt(5))^n))/80 \\ _Colin Barker_, Jul 25 2016
%Y A157459 Cf. A007805, A049629, A157014, A157459, A201003, A298271.
%K A157459 nonn,easy
%O A157459 1,2
%A A157459 _Paul Weisenhorn_, Mar 01 2009
%E A157459 Edited by _Alois P. Heinz_, Sep 09 2011