A372221 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, I, X.

1, 1, 1, 1, 1, 2, 3, 6, 9, 12, 16, 21, 41, 66, 106, 156, 219, 364, 558, 930, 1444, 2191, 3515, 5361, 8737, 13661, 21478, 34397, 53528, 86137, 135294, 215432, 345081, 546705, 879212, 1395476, 2239086, 3596427, 5767656, 9312008, 14949738, 24163742, 39045229

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..4472

Alois P. Heinz, G.f. for A372221

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, order 139.

Example

a(7) = 6:
   ._____________.   ._____________.   ._____________.
   | |_________| |   | | | | | | | |   |_________| | |
   | .___| |___. |   | | | | | | | |   |_________| | |
   |_| ._| |_. |_|   | | | | | | | |   |_________| | |
   | ._|_____|_. |   | | | | | | | |   |_________| | |
   |_|_________|_|   |_|_|_|_|_|_|_|   |_________|_|_|
   ._____________.   ._____________.   ._____________.
   | |_________| |   | |_________| |   | | |_________|
   |_. |_. ._| ._|   | |_________| |   | | |_________|
   | |___| |___| |   | |_________| |   | | |_________|
   | .___|_|___. |   | |_________| |   | | |_________|
   |_|_________|_|   |_|_________|_|   |_|_|_________| .

Crossrefs

Cf. A003520, A174249, A366324.

Sequence in context: A140495 A174873 A213172 * A008810 A280984 A339485

Adjacent sequences: A372218 A372219 A372220 * A372222 A372223 A372224

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 22 2024

Status

approved