A352432 Number of tilings of a 4 X n rectangle using dominoes and 2 X 2 tiles.

1, 1, 11, 29, 165, 593, 2773, 11093, 48605, 201829, 864901, 3638261, 15472261, 65377669, 277294885, 1173523013, 4972873413, 21056700293, 89200845765, 377774394309, 1600161267781, 6777276186821, 28705824305861, 121582507360709

Offset

0,3

Comments

The sequence is based on A352431.

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (3,10,-18,-14,20).

Formula

G.f.:(1 - 2*x - 2*x^2 + 4*x^3)/(1 - 3*x - 10*x^2 + 18*x^3 + 14*x^4 - 20*x^5).

a(n) = 3*a(n-1) + 10*a(n-2) - 18*a(n-3) - 14*a(n-4) + 20*a(n-5).

Example

a(2)=11:
   ___     ___     ___     ___     ___     ___
  |   |   |   |   |   |   | | |   |___|   |___|
  |___|   |___|   |___|   |_|_|   |___|   |___|
  |   |   | | |   |___|   |   |   |   |   |___|
  |___|   |_|_|   |___|   |___|   |___|   |___|
.
       ___     ___     ___     ___     ___
      |___|   | | |   |___|   |___|   | | |
      |   |   |_|_|   | | |   |___|   |_|_|
      |___|   | | |   |_|_|   | | |   |___|
      |___|   |_|_|   |___|   |_|_|   |___|

Crossrefs

Cf. A352431, A352433.

Sequence in context: A080083 A115972 A099109 * A302091 A122095 A282137

Adjacent sequences: A352429 A352430 A352431 * A352433 A352434 A352435

Keyword

nonn

Author

Gerhard Kirchner, Mar 17 2022

Status

approved