A364460 Number of tilings of a 3 X n rectangle using dominoes and trominoes (of any shape).

1, 1, 6, 30, 145, 733, 3540, 17300, 84479, 411963, 2011408, 9816506, 47911847, 233851991, 1141365064, 5570761346, 27189615925, 132706261547, 647709321582, 3161321546320, 15429691961077, 75308819284819, 367565220881250, 1794002281279416, 8756117243124305, 42736617464745197

Offset: 0

Author

Alois P. Heinz, Jul 25 2023

Keywords

• nonn
• easy

Examples

			a(2) = 6:
  .___.   .___.   .___.   .___.   .___.   .___.
  | | |   |___|   | | |   |___|   | ._|   |_. |
  | | |   |___|   |_|_|   | | |   |_| |   | |_|
  |_|_|   |___|   |___|   |_|_|   |___|   |___|  .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1453
• Wikipedia, Domino (mathematics)
• Wikipedia, Tromino
• Index entries for linear recurrences with constant coefficients, signature (3,6,13,0,53,18,69,48,35,-125,-76,-24,38,8,18,1,-3,-1).

Crossrefs

Column k=3 of A364457.

Cf. A133872.

Formula

G.f.: -(x^15 +2*x^14 +4*x^13 -5*x^12 -9*x^11 -18*x^10 +16*x^9 +5*x^8 +8*x^7 -10*x^6 +13*x^5 -6*x^4 +7*x^3 +3*x^2 +2*x -1) / (x^18 +3*x^17 -x^16 -18*x^15 -8*x^14 -38*x^13 +24*x^12 +76*x^11 +125*x^10 -35*x^9 -48*x^8 -69*x^7 -18*x^6 -53*x^5 -13*x^3 -6*x^2 -3*x +1).

a(n) mod 2 = A133872(n).