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 A156095 #8 Feb 10 2014 01:32:34 %S A156095 1,11,61,361,2311,15401,104401,712531,4875781,33398201,228859951, %T A156095 1568486161,10750188961,73681909211,505020747661,3461456968201, %U A156095 23725161388951,162614629188281,1114577128871281,7639424974303651,52361396909490901 %N A156095 5 F(2n) (F(2n) + 1) + 1 where F(n) denotes the n-th Fibonacci number. %C A156095 Natural bilateral extension (brackets mark index 0): ..., 14851, 2101, 281, 31, 1, [1], 11, 61, 361, 2311, 15401, ... This is A156095-reversed followed by A156095, without repeating the central 1. That is, A156095(-n) = A156094(n). %F A156095 Let F(n) be the Fibonacci number A000045(n) and let L(n) be the Lucas number A000032(n). %F A156095 Alternate formula: a(n) = L(4n) + 5 F(2n) - 1. %F A156095 Recurrence: a(n) - 10 a(n-1) + 23 a(n-2) - 10 a(n-3) + a(n-4) = -5. %F A156095 Recurrence: a(n) - 11 a(n-1) + 33 a(n-2) - 33 a(n-3) + 11 a(n-4) - a(n-5) = 0. %F A156095 G.f.: A(x) = (1 - 27 x^2 + 20 x^3 + x^4)/(1 - 11 x + 33 x^2 - 33 x^3 + 11 x^4 - x^5) = (1 - 27 x^2 + 20 x^3 + x^4)/((1 - x) (1 - 7 x + x^2) (1 - 3 x + x^2)). %F A156095 a(n)=((2*sqrt(5))/2)*(((3+sqrt(5))/2)^n-((3-sqrt(5))/2)^n)+((7+3*sqrt(5))/2)^n+((7-3*sqrt(5))/2)^n-1. - _Tim Monahan_, Aug 15 2011 %t A156095 a[n_Integer] := 5 Fibonacci[2n] (Fibonacci[2n] + 1) + 1 %Y A156095 Cf. A124296, A124297, A001603, A001604, A156094. %K A156095 nonn,easy %O A156095 0,2 %A A156095 _Stuart Clary_, Feb 04 2009