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

Offset

0,3

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).

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).

Example

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

Crossrefs

Column k=3 of A364457.

Cf. A133872.

Sequence in context: A307494 A316593 A089817 * A006320 A319377 A079738

Adjacent sequences: A364457 A364458 A364459 * A364461 A364462 A364463

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 25 2023

Status

approved