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 A157878 #20 Sep 05 2021 15:01:29
%S A157878 1,31,929,27839,834241,24999391,749147489,22449425279,672733610881,
%T A157878 20159558901151,604114033423649,18103261443808319,542493729280825921,
%U A157878 16256708616980969311,487158764780148253409,14598506234787466632959,437468028278843850735361
%N A157878 Expansion of x*(1+x)/(x^2-30*x+1).
%C A157878 This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:
%C A157878 A * c(n)+1 = a(n)^2,
%C A157878 (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
%C A157878 this is the b(n) sequence for A=7.
%H A157878 Robert Israel, <a href="/A157878/b157878.txt">Table of n, a(n) for n = 1..610</a>
%H A157878 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (30,-1).
%F A157878 G.f.: x*(1+x)/(x^2-30*x+1).
%F A157878 a(1) = 1, a(2) = 31, a(n) = 30*a(n-1)-a(n-2) for n>2.
%F A157878 a(n) = ((15-4*sqrt(14))^(n-1)*(7-2*sqrt(14))+(7+2*sqrt(14))*(15+4*sqrt(14))^(n-1))/14. - _Gerry Martens_, Jul 09 2015
%p A157878 f:= gfun:-rectoproc({a(1) = 1, a(2) = 31, a(n) = 30*a(n-1)-a(n-2)}, a(n), remember):
%p A157878 map(f, [$1..30]); # _Robert Israel_, Jul 09 2015
%t A157878 CoefficientList[Series[x*(1 + x)/(x^2 - 30 x + 1), {x, 0, 17}], x] (* _Michael De Vlieger_, Jul 09 2015 *)
%t A157878 LinearRecurrence[{30,-1},{1,31},20] (* _Harvey P. Dale_, Sep 05 2021 *)
%o A157878 (PARI) Vec((1+x)/(x^2-30*x+1)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 25 2012
%Y A157878 7*A157879(n)+1 = A157877(n)^2.
%Y A157878 8*A157879(n)+1 = A157878(n)^2.
%K A157878 nonn,easy
%O A157878 1,2
%A A157878 _Paul Weisenhorn_, Mar 08 2009
%E A157878 Edited by _Alois P. Heinz_, Sep 09 2011