A355883 Number of ways to 5-color a 3 X n grid ignoring the variations of two colors.

4, 169, 7141, 301741, 12749989, 538747549, 22764640981, 961914128461, 40645437426949, 1717462645311229, 72570948297479221, 3066467006530462381, 129572785291363217509, 5475065165353811151709, 231347489347123368595861, 9775529461439509493215501

Offset: 1

Author

Gerhard Kirchner, Jul 24 2022

Keywords

• nonn
• easy

Comments

See A355881 for a general formula.

Examples

			a(1) = 4, 5 colors 1,2,3,4,5: 121, 123, 124, 125.
The first two colors do not vary.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..600
• Index entries for linear recurrences with constant coefficients, signature (45,-116).

Crossrefs

Cf. A355881, A355882.

Programs

Mathematica

LinearRecurrence[{45, -116}, {4, 169}, 20] (* Paolo Xausa, Oct 03 2024 *)

Formula

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

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

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

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