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 A048878 #32 May 25 2024 15:33:09
%S A048878 1,9,37,157,665,2817,11933,50549,214129,907065,3842389,16276621,
%T A048878 68948873,292072113,1237237325,5241021413,22201322977,94046313321,
%U A048878 398386576261,1687592618365,7148757049721,30282620817249,128279240318717,543399582092117,2301877568687185
%N A048878 Generalized Pellian with second term of 9.
%H A048878 Harry J. Smith, <a href="/A048878/b048878.txt">Table of n, a(n) for n = 0..1584</a>
%H A048878 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A048878 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,1).
%F A048878 a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5).
%F A048878 G.f.: (1+5*x)/(1-4*x-x^2). - _Philippe Deléham_, Nov 03 2008
%F A048878 a(n) = F(3*n+3) + F(3*n-2); F = A000045. - Yomna Bakr and _Greg Dresden_, May 25 2024
%e A048878 a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9.
%p A048878 with(combinat): a:=n->5*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # _Zerinvary Lajos_, Apr 04 2008
%t A048878 LinearRecurrence[{4,1},{1,9},31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2),{x,0,30}],x] (* _Harvey P. Dale_, Jul 12 2011 *)
%o A048878 (PARI) { default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ _Harry J. Smith_, May 31 2009
%Y A048878 Cf. A000045, A015448, A001077, A001076, A033887.
%K A048878 nonn,easy,nice
%O A048878 0,2
%A A048878 _Barry E. Williams_