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 A271357 #24 Sep 08 2022 08:46:16
%S A271357 3,10,27,71,186,487,1275,3338,8739,22879,59898,156815,410547,1074826,
%T A271357 2813931,7366967,19286970,50493943,132194859,346090634,906077043,
%U A271357 2372140495,6210344442,16258892831,42566334051,111440109322,291753993915,763821872423,1999711623354
%N A271357 a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=3.
%H A271357 Colin Barker, <a href="/A271357/b271357.txt">Table of n, a(n) for n = 0..1000</a>
%H A271357 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1).
%F A271357 G.f.: (3+x) / (1-3*x+x^2).
%F A271357 a(n) = 3*a(n-1)-a(n-2) for n>1.
%F A271357 a(n) = (2^(-2-n)*((9-sqrt(5))*(3+sqrt(5))^(n+1) - (9+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5).
%F A271357 a(n) = 4*Fibonacci(2*n+2) - Fibonacci(2*n+1).
%t A271357 Table[3Fibonacci[2n+1]+4Fibonacci[2n],{n,0,30}] (* or *) LinearRecurrence[ {3,-1},{3,10},30] (* _Harvey P. Dale_, Apr 05 2019 *)
%o A271357 (PARI) a(n) = 3*fibonacci(2*n+1) + 4*fibonacci(2*n)
%o A271357 (PARI) Vec((3+x)/(1-3*x+x^2) + O(x^50))
%o A271357 (Magma) k:=3; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // _Bruno Berselli_, Apr 06 2016
%Y A271357 Cf. A000045.
%Y A271357 Cf. A001906 (k=0), A002878 (k=1), A100545 (k=2, without the initial 2), this sequence (k=3), A271358 (k=4), A271359 (k=5).
%K A271357 nonn,easy
%O A271357 0,1
%A A271357 _Colin Barker_, Apr 05 2016
%E A271357 Changed offset and adapted definition, programs and formulas by _Bruno Berselli_, Apr 06 2016