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 A210678 #30 Mar 28 2024 16:11:42
%S A210678 1,1,6,12,24,43,75,127,212,350,574,937,1525,2477,4018,6512,10548,
%T A210678 17079,27647,44747,72416,117186,189626,306837,496489,803353,1299870,
%U A210678 2103252,3403152,5506435,8909619,14416087,23325740,37741862,61067638,98809537,159877213,258686789,418564042
%N A210678 a(n) = a(n-1)+a(n-2)+n+2, a(0)=a(1)=1.
%H A210678 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).
%F A210678 From _Colin Barker_, Jun 30 2012: (Start)
%F A210678 a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4).
%F A210678 G.f.: (1 -2*x + 5*x^2 - 3*x^3)/((1 - x)^2*(1 - x - x^2)). (End)
%t A210678 LinearRecurrence[{3,-2,-1,1},{1,1,6,12},40] (* _Harvey P. Dale_, Dec 10 2014 *)
%t A210678 nxt[{n_,a_,b_}]:={n+1,b,a+b+n+3}; NestList[nxt,{1,1,1},40][[;;,2]] (* _Harvey P. Dale_, Mar 19 2023 *)
%Y A210678 Cf. A081659: a(n)=a(n-1)+a(n-2)+n-5, a(0)=a(1)=1 (except first 2 terms and sign).
%Y A210678 Cf. A001924: a(n)=a(n-1)+a(n-2)+n-4, a(0)=a(1)=1 (except first 4 terms).
%Y A210678 Cf. A000126: a(n)=a(n-1)+a(n-2)+n-2, a(0)=a(1)=1 (except first term).
%Y A210678 Cf. A066982: a(n)=a(n-1)+a(n-2)+n-1, a(0)=a(1)=1.
%Y A210678 Cf. A030119: a(n)=a(n-1)+a(n-2)+n, a(0)=a(1)=1.
%Y A210678 Cf. A210677: a(n)=a(n-1)+a(n-2)+n+1, a(0)=a(1)=1.
%K A210678 nonn,easy
%O A210678 0,3
%A A210678 _Alex Ratushnyak_, May 09 2012