A278874 Number of tilings of a 2 X n rectangle using pentominoes of any shape and monominoes.

1, 1, 1, 7, 25, 50, 155, 508, 1343, 3800, 11438, 32525, 92333, 268766, 774302, 2216976, 6392865, 18425916, 52958070, 152425812, 438973764, 1263109849, 3634965137, 10463959311, 30116734921, 86675829307, 249478723992, 718056248229, 2066658063664, 5948257601097

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Pentomino

Formula

G.f.: -(x^10 +x^8 -x^6 -6*x^5 -x^4 -5*x^3 +1) / (x^15 +x^13 -2*x^11 -11*x^10 -2*x^9 -10*x^8 +x^7 +9*x^6 +12*x^5 +8*x^4 +11*x^3 +x -1).

Example

a(3) = 7:
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_|_|_| | |_| | | ._. | |   ._| |_.   | |   |_| |_|   |
|_|_|_| |_____| |_|_|_| |___|_| |_|___| |_____| |_____| .

Crossrefs

Column k=2 of A278657.

Sequence in context: A147129 A173825 A269589 * A137380 A309901 A094672

Adjacent sequences: A278871 A278872 A278873 * A278875 A278876 A278877

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 29 2016

Status

approved