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 A154964 #35 Dec 31 2023 10:24:59
%S A154964 1,1,5,21,93,405,1773,7749,33885,148149,647757,2832165,12383037,
%T A154964 54142101,236724525,1035026181,4525425693,19786434165,86511856653,
%U A154964 378254174949,1653833664765,7231026043989,31616080120557,138234396625605,604399670600157,2642605391554101
%N A154964 a(n) = 3*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=1, a(2)=5.
%C A154964 For n>=1, a(n) is the number of words of length n-1 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively. - _Armend Shabani_, Mar 01 2017
%H A154964 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,6).
%F A154964 G.f.: (1 - 2*x - 4*x^2)/(1 - 3*x - 6*x^2).
%F A154964 a(n+1) = Sum_{k=0..n} A154929(n,k)*2^(n-k).
%F A154964 G.f.: Q(0)/6 +2/3 , where Q(k) = 1 + 1/(1 - x*(6*k+3 + 6*x )/( x*(6*k+6 + 6*x ) + 1/Q(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Sep 21 2013
%F A154964 a(n) = A083858(n+1)/3, n>=1. - _R. J. Mathar_, Feb 06 2020
%t A154964 {1}~Join~LinearRecurrence[{3, 6}, {1, 5}, 25] (* or *)
%t A154964 CoefficientList[Series[(1 - 2 x - 4 x^2)/(1 - 3 x - 6 x^2), {x, 0, 25}], x] (* _Michael De Vlieger_, Mar 02 2017 *)
%o A154964 (PARI) Vec((1-2*x-4*x^2)/(1-3*x-6*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 11 2012
%K A154964 nonn,easy
%O A154964 0,3
%A A154964 _Philippe Deléham_, Jan 18 2009