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 A157877 #74 May 04 2025 09:33:17
%S A157877 1,29,869,26041,780361,23384789,700763309,20999514481,629284671121,
%T A157877 18857540619149,565096933903349,16934050476481321,507456417360536281,
%U A157877 15206758470339607109,455695297692827676989,13655652172314490702561,409213869871741893399841
%N A157877 Expansion of (1-x)*x/(x^2-30*x+1).
%C A157877 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 A157877 A * c(n)+1 = a(n)^2,
%C A157877 (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
%C A157877 A157877 is the a(n) sequence for A=7.
%C A157877 Positive values of x (or y) satisfying x^2 - 30xy + y^2 + 28 = 0. - _Colin Barker_, Feb 23 2014
%H A157877 Vincenzo Librandi, <a href="/A157877/b157877.txt">Table of n, a(n) for n = 1..200</a>
%H A157877 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (30,-1).
%F A157877 G.f.: (1-x)*x/(x^2-30*x+1).
%F A157877 a(1)=1, a(2)=29; for n>2, a(n) = 30*a(n-1)-a(n-2).
%F A157877 7*A157879(n)+1 = a(n)^2.
%F A157877 8*A157879(n)+1 = A157878(n)^2.
%F A157877 a(n) = (1/8)*(4-sqrt(14))*(1+(15+4*sqrt(14))^(2*n-1))/(15+4*sqrt(14))^(n-1). - _Bruno Berselli_, Feb 25 2014
%F A157877 From _Andrea Pinos_, Oct 05 2022: (Start)
%F A157877 a(n) = ceiling((C^n)/(C+1)), where C = 15 + 4*sqrt(14) = sqrt(225) + sqrt(224).
%F A157877 Limit_{n->oo} a(n+1)/a(n) = C. (End)
%t A157877 LinearRecurrence[{30,-1},{1,29},30] (* _Harvey P. Dale_, Dec 14 2011 *)
%t A157877 CoefficientList[Series[(1 - x)/(x^2 - 30 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 25 2014 *)
%o A157877 (PARI) Vec((1-x)*x/(x^2-30*x+1)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 25 2012
%o A157877 (Magma) I:=[1,29,869]; [n le 3 select I[n] else 30*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Feb 25 2014
%Y A157877 Cf. A157879, A157877, A157878.
%Y A157877 Cf. similar sequences listed in A238379.
%K A157877 nonn,easy
%O A157877 1,2
%A A157877 _Paul Weisenhorn_, Mar 08 2009
%E A157877 Edited by _Alois P. Heinz_, Sep 09 2011