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 A083101 #29 Jan 12 2025 12:59:00
%S A083101 1,12,34,188,716,3312,13784,60688,259216,1125312,4842784,20938688,
%T A083101 90305216,389997312,1683046784,7266066688,31362601216,135385869312,
%U A083101 584397750784,2522654194688,10889285897216,47005113741312,202903086454784,875857310322688,3780745485193216
%N A083101 a(n) = 2*a(n-1) + 10*a(n-2), with a(0) = 1, a(1) = 12.
%C A083101 a(n)/A083102(n) converges to sqrt(11).
%C A083101 a(n-1) is the number of compositions of n when there are 1 type of 1 and 11 types of other natural numbers. - _Milan Janjic_, Aug 13 2010
%C A083101 A133294 is an essentially identical sequence (with a different start). - _N. J. A. Sloane_, Dec 31 2012
%H A083101 G. C. Greubel, <a href="/A083101/b083101.txt">Table of n, a(n) for n = 0..1000</a>
%H A083101 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,10).
%F A083101 a(n+1) = a(n) + 11*A083102(n).
%F A083101 G.f.: (1+10*x)/(1-2*x-10*x^2).
%F A083101 If p[1]=1, and p[i]=11, (i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=det A. - _Milan Janjic_, Apr 29 2010
%t A083101 CoefficientList[Series[(1+10x)/(1-2x-10x^2), {x, 0, 25}], x]
%t A083101 LinearRecurrence[{2, 10},{1, 12},22] (* _Ray Chandler_, Sep 23 2015 *)
%o A083101 (PARI) x='x+O('x^30); Vec((1+10*x)/(1-2*x-10*x^2)) \\ _G. C. Greubel_, Jan 08 2018
%o A083101 (Magma) I:=[1,12]; [n le 2 select I[n] else 2*Self(n-1) + 10*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 08 2018
%Y A083101 Cf. A083102, A133294.
%K A083101 easy,nonn
%O A083101 0,2
%A A083101 Mario Catalani (mario.catalani(AT)unito.it), Apr 22 2003