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 A271358 #32 Sep 08 2022 08:46:16 %S A271358 4,13,35,92,241,631,1652,4325,11323,29644,77609,203183,531940,1392637, %T A271358 3645971,9545276,24989857,65424295,171283028,448424789,1173991339, %U A271358 3073549228,8046656345,21066419807,55152603076,144391389421,378021565187,989673306140 %N A271358 a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=4. %H A271358 Colin Barker, <a href="/A271358/b271358.txt">Table of n, a(n) for n = 0..1000</a> %H A271358 Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M. <a href="https://doi.org/10.1007/s10801-011-0327-z">On the cyclically fully commutative elements of Coxeter groups</a>, J. Algebr. Comb. 36, No. 1, 123-148 (2012) Table 1 CFC Type D. %H A271358 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1). %F A271358 G.f.: (4+x) / (1-3*x+x^2). %F A271358 a(n) = 3*a(n-1)-a(n-2) for n>1. %F A271358 a(n) = (2^(-2-n)*((11-sqrt(5))*(3+sqrt(5))^(n+1) - (11+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5). %F A271358 a(n) = 5*Fibonacci(2*n+2) - Fibonacci(2*n+1). %F A271358 a(n) = 4*A001906(n+1) + A001906(n-1). %o A271358 (PARI) a(n) = 4*fibonacci(2*n+1) + 5*fibonacci(2*n) %o A271358 (PARI) Vec((4+x)/(1-3*x+x^2) + O(x^50)) %o A271358 (Magma) k:=4; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // _Bruno Berselli_, Apr 06 2016 %Y A271358 Cf. A000045. %Y A271358 Cf. A001906 (k=0), A002878 (k=1), A100545 (k=2, without the initial 2), A271357 (k=3), this sequence (k=4), A271359 (k=5). %K A271358 nonn,easy %O A271358 0,1 %A A271358 _Colin Barker_, Apr 05 2016 %E A271358 Changed offset and adapted definition, programs and formulas by _Bruno Berselli_, Apr 06 2016