A355882 - OEIS

%I #15 Oct 04 2024 00:27:45

%S 3,49,801,13095,214083,3499929,57218481,935434575,15292923363,

%T 250015887009,4087377035361,66822357687255,1092443258415843,

%U 17859774993929289,291979981913499441,4773425749606899135,78038203981259699523,1275805176423288314769

%N Number of ways to 4-color a 3 X n grid ignoring the variations of two colors.

%C See A355881 for a general formula.

%H Paolo Xausa, <a href="/A355882/b355882.txt">Table of n, a(n) for n = 1..800</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-27).

%F G.f.: x*(3-5*x)/(1-18*x+27*x^2).

%F a(n) = 18*a(n-1) - 27*a(n-2) with a(1) = 3, a(2) = 49.

%F 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 a(n) = 2*A198710(n) - 1. - _Hugo Pfoertner_,  Jul 24 2022

%e a(1) = 3, 4 colors 1,2,3,4: 121, 123, 124.

%e The first two colors do not vary.

%t LinearRecurrence[{18, -27}, {3, 49}, 20] (* _Paolo Xausa_, Oct 03 2024 *)

%Y Cf. A198710, A355881, A355883.

%K nonn,easy

%O 1,1

%A _Gerhard Kirchner_, Jul 24 2022