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

Author

Alois P. Heinz, Nov 29 2016

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Column k=2 of A278657.

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).