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 A048877 #31 Jun 13 2015 00:50:00 %S A048877 1,8,33,140,593,2512,10641,45076,190945,808856,3426369,14514332, %T A048877 61483697,260449120,1103280177,4673569828,19797559489,83863807784, %U A048877 355252790625,1504874970284,6374752671761 %N A048877 a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=8. %C A048877 Generalized Pellian with second term of 8. %H A048877 Reinhard Zumkeller, <a href="/A048877/b048877.txt">Table of n, a(n) for n = 0..1000</a> %H A048877 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a> %H A048877 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,1). %F A048877 a(n) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)). %F A048877 G.f.: (1+4*x)/(1-4*x-x^2). - _Philippe Deléham_, Nov 03 2008 %F A048877 a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8. %p A048877 with(combinat): a:=n->4*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # _Zerinvary Lajos_, Apr 04 2008 %t A048877 CoefficientList[Series[(1+4x)/(1-4x-x^2),{x,0,20}],x] (* _Harvey P. Dale_, Mar 30 2011 *) %t A048877 LinearRecurrence[{4,1},{1,8},30] (* _Harvey P. Dale_, Nov 03 2013 *) %o A048877 (Haskell) %o A048877 a048877 n = a048877_list !! n %o A048877 a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list) %o A048877 -- _Reinhard Zumkeller_, May 01 2013 %Y A048877 Cf. A015448, A001076, A001077, A033887. %K A048877 easy,nonn %O A048877 0,2 %A A048877 _Barry E. Williams_