A353965 Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles and right trominoes.

1, 1, 13, 47, 259, 1189, 5877, 28167, 136723, 660173, 3194613, 15445007, 74699811, 361230229, 1746933205, 8448061879, 40854753875, 197572345789, 955455626773, 4620559362303, 22344915889827, 108059470995013, 522573007884725, 2527150465444071, 12221238828079379

Offset: 0

Author

Gerhard Kirchner, May 13 2022

Keywords

• nonn
• easy

Comments

For tiling algorithm see A351322.

Examples

			a(2) = 13:
    v    h,v   h=v   h,v
   ___   ___   ___   ___   ___
  |   | | |_| |  _| |  _| |_|_|    mirroring included
  |___| |___| |_| | |_|_| |_|_|    h: horizontal, v: vertical
  |_|_| |_|_| |___| |_|_| |_|_|
    2  +  4  +  2  +  4  +  1 = 13
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,9,-1,2).

Crossrefs

Cf. A351322, A352589, A353963, A353964.

Programs

Maxima

See A352589.

Formula

G.f.: (1 - 2*x + x^2) / (1 - 3*x - 9*x^2 + x^3 - 2*x^4).

a(n) = 3*a(n-1) + 9*a(n-2) - a(n-3) + 2*a(n-4).

31*a(n) = 18*(-2)^n +13*A200739(n+3) +2*A200739(n+2) +9*A200739(n+1). - R. J. Mathar, Jun 07 2025