A376031 Number of ways to tile a 3 x (2*n) rectangle with dominoes and T's.

1, 3, 18, 112, 692, 4294, 26624, 165086, 1023662, 6347440, 39358774, 244053158, 1513307844, 9383614226, 58185263358, 360791140032, 2237168644134, 13872079956206, 86017029971684, 533368425534858, 3307273890427894, 20507514248408832, 127161570097317790

Offset: 0

Author

Greg Dresden and Lucas MingQu Xia, Sep 06 2024

Keywords

• nonn
• easy

Comments

a(n) is the number of ways to tile a 3 X (2*n) rectangle with two kinds of tiles: dominoes (made up of 2 cells) and T's (made up of 4 cells), each of which can be rotated as needed.

Examples

			For n=3, here is one of the a(3) = 112 ways to tile a 3 x 6 rectangle using our dominoes and T's:
 ___________
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Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,7,4,-8,2).

Crossrefs

Cf. A033506, A219968, A337492, A346054.

Programs

Mathematica

LinearRecurrence[{5, 7, 4, -8, 2}, {1, 3, 18, 112, 692}, 30] (* Paolo Xausa, Sep 23 2024 *)

Formula

a(n) = 5*a(n-1) + 7*a(n-2) + 4*a(n-3) - 8*a(n-4) + 2*a(n-5).

G.f.: -(2*x^4-3*x^3-4*x^2-2*x+1)/(2*x^5-8*x^4+4*x^3+7*x^2+5*x-1).