A352789 Number of ways to tile a 3 X n strip with squares and P-shaped heptominoes.

1, 1, 1, 9, 17, 27, 101, 239, 473, 1315, 3281, 7267, 18265, 45459, 106225, 258907, 637113, 1523443, 3685617, 8994971, 21700329, 52459491, 127466145, 308440011, 746105881, 1809235699, 4381674769, 10605454107, 25696219721, 62241829635, 150703933889, 365037041195

Offset

0,4

Comments

a(n) is also the number of ways to tile a 1 X n strip with squares, eight colors of trominoes, and 2 colors of pentominoes.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (1,0,8,0,2).

Formula

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

G.f.: 1/(1 - x - 8*x^3 - 2*x^5). - Stefano Spezia, Apr 03 2022

Example

The a(3) = 9 solutions are as follows:
   _____   _____   _____
  |_|_|_| |   |_| |_|   |
  |_|_|_| |   |_| |_|   |
  |_|_|_| |_____| |_____|
   _____   _____   _____
  |_    | |    _| | |_|_|
  |_|   | |   |_| |     |
  |_|___| |___|_| |_____|
   _____   _____   _____
  |_|_| | |     | |     |
  |     | |_ _  | |  _ _|
  |_____| |_|_|_| |_|_|_|

Mathematica

LinearRecurrence[{1, 0, 8, 0, 2}, {1, 1, 1, 9, 17}, 34];

Crossrefs

Sequence in context: A235361 A109333 A081030 * A285009 A228260 A147459

Adjacent sequences: A352786 A352787 A352788 * A352790 A352791 A352792

Keyword

nonn,easy

Author

Drisana Bhatia, Apr 03 2022

Status

approved