A355883 - OEIS

%I #13 Oct 04 2024 00:27:35

%S 4,169,7141,301741,12749989,538747549,22764640981,961914128461,

%T 40645437426949,1717462645311229,72570948297479221,

%U 3066467006530462381,129572785291363217509,5475065165353811151709,231347489347123368595861,9775529461439509493215501

%N Number of ways to 5-color a 3 X n grid ignoring the variations of two colors.

%C See A355881 for a general formula.

%H Paolo Xausa, <a href="/A355883/b355883.txt">Table of n, a(n) for n = 1..600</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (45,-116).

%F a(n) = A222139(n)/4.

%F G.f.: x*(4-11*x)/(1-45*x+116*x^2).

%F a(n) = 45*a(n-1) - 116*a(n-2) with a(1) = 4, a(2) = 169.

%F a(n) = 2^(-3-n)*((45 - sqrt(1561))^n*(11*sqrt(1561) - 433) + (45 + sqrt(1561))^n*(11*sqrt(1561) + 433))/(29*sqrt(1561)). - _Stefano Spezia_, Jul 24 2022

%e a(1) = 4, 5 colors 1,2,3,4,5: 121, 123, 124, 125.

%e The first two colors do not vary.

%t LinearRecurrence[{45, -116}, {4, 169}, 20] (* _Paolo Xausa_, Oct 03 2024 *)

%Y Cf. A355881, A355882.

%K nonn,easy

%O 1,1

%A _Gerhard Kirchner_, Jul 24 2022