login
A278874
Number of tilings of a 2 X n rectangle using pentominoes of any shape and monominoes.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Nov 29 2016
STATUS
approved