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 A355882 #18 Mar 22 2025 23:34:48
%S A355882 3,49,801,13095,214083,3499929,57218481,935434575,15292923363,
%T A355882 250015887009,4087377035361,66822357687255,1092443258415843,
%U A355882 17859774993929289,291979981913499441,4773425749606899135,78038203981259699523,1275805176423288314769
%N A355882 Number of ways to 4-color a 3 X n grid ignoring the variations of two colors.
%C A355882 See A355881 for a general formula.
%H A355882 Paolo Xausa, <a href="/A355882/b355882.txt">Table of n, a(n) for n = 1..800</a>
%H A355882 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-27).
%F A355882 G.f.: x*(3-5*x)/(1-18*x+27*x^2).
%F A355882 a(n) = 18*a(n-1) - 27*a(n-2) with a(1) = 3, a(2) = 49.
%F A355882 a(n) = 3^(n-7/2)*((12 + 5*sqrt(6))*(3 + sqrt(6))^n - (3 - sqrt(6))^n*(12 - 5*sqrt(6)))/(2*sqrt(2)). - _Stefano Spezia_, Jul 24 2022
%F A355882 a(n) = 2*A198710(n) - 1. - _Hugo Pfoertner_, Jul 24 2022
%e A355882 a(1) = 3, 4 colors 1,2,3,4: 121, 123, 124.
%e A355882 The first two colors do not vary.
%t A355882 LinearRecurrence[{18, -27}, {3, 49}, 20] (* _Paolo Xausa_, Oct 03 2024 *)
%Y A355882 Cf. A198710, A355881, A355883.
%K A355882 nonn,easy
%O A355882 1,1
%A A355882 _Gerhard Kirchner_, Jul 24 2022