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 A022314 #28 Aug 25 2017 23:35:14
%S A022314 0,9,10,20,31,52,84,137,222,360,583,944,1528,2473,4002,6476,10479,
%T A022314 16956,27436,44393,71830,116224,188055,304280,492336,796617,1288954,
%U A022314 2085572,3374527,5460100,8834628,14294729,23129358,37424088,60553447,97977536,158530984
%N A022314 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0, a(1) = 9.
%H A022314 Vincenzo Librandi, <a href="/A022314/b022314.txt">Table of n, a(n) for n = 0..1000</a>
%H A022314 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F A022314 a(n) = -1 + (1/2)*((1 + sqrt(5))/2)^n + (19/10)sqrt(5)*((1 + sqrt(5))/2)^n - (19/10)*sqrt(5)*((1 - sqrt(5))/2)^n + (1/2)*((1 - sqrt(5))/2)^n, obtained using PURRS. - _Alexander R. Povolotsky_, Apr 22 2008
%F A022314 From _R. J. Mathar_, Apr 07 2011: (Start)
%F A022314 G.f.: -x*(-9+8*x) / ( (x-1)*(x^2+x-1) ).
%F A022314 a(n) = A022100(n) - 1. (End)
%F A022314 a(n) = F(n+2) + 8*F(n) - 1, where A000045. - _G. C. Greubel_, Aug 25 2017
%e A022314 G.f. = 9*x + 10*x^2 + 20*x^3 + 31*x^4 + 52*x^5 + 84*x^6 + 137*x^7 + 222*x^8 + ...
%t A022314 LinearRecurrence[{2, 0, -1}, {0, 9, 10}, 60] (* _Vladimir Joseph Stephan Orlovsky_, Feb 11 2012 *)
%t A022314 a[ n_] := 9 Fibonacci[n] + Fibonacci[n + 1] - 1; (* _Michael Somos_, Nov 21 2016 *)
%o A022314 (PARI) concat(0, Vec(-x*(-9+8*x) / ( (x-1)*(x^2+x-1) ) + O(x^30))) \\ _Michel Marcus_, Nov 20 2016
%o A022314 {a(n) = 9*fibonacci(n) + fibonacci(n+1) - 1}; /* _Michael Somos_, Nov 21 2016 */
%Y A022314 Cf. A022100.
%K A022314 nonn
%O A022314 0,2
%A A022314 _N. J. A. Sloane_