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 A022313 #23 Nov 23 2017 16:00:13
%S A022313 0,8,9,18,28,47,76,124,201,326,528,855,1384,2240,3625,5866,9492,15359,
%T A022313 24852,40212,65065,105278,170344,275623,445968,721592,1167561,1889154,
%U A022313 3056716,4945871,8002588,12948460,20951049,33899510,54850560,88750071,143600632
%N A022313 a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 8.
%H A022313 Vincenzo Librandi, <a href="/A022313/b022313.txt">Table of n, a(n) for n = 0..1000</a>
%H A022313 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F A022313 From _R. J. Mathar_, Apr 07 2011: (Start)
%F A022313 G.f.: x*(8-7*x)/( (1-x)*(1-x-x^2) ).
%F A022313 a(n) = A022099(n) - 1. (End)
%F A022313 a(n) = F(n+2) + 7*F(n) - 1, where F = A000045. - _G. C. Greubel_, Aug 25 2017
%t A022313 LinearRecurrence[{2, 0, -1}, {0, 8, 9}, 60] (* _Vladimir Joseph Stephan Orlovsky_, Feb 11 2012 *)
%t A022313 RecurrenceTable[{a[0]==0,a[1]==8,a[n]==a[n-1]+a[n-2]+1},a,{n,40}] (* _Harvey P. Dale_, Nov 23 2017 *)
%o A022313 (PARI) x='x+O('x^50); concat([0], Vec(x*(8-7*x)/( (1-x)*(1-x-x^2) ))) \\ _G. C. Greubel_, Aug 25 2017
%K A022313 nonn
%O A022313 0,2
%A A022313 _N. J. A. Sloane_