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A349187
Number of tilings of a 5 X n rectangle using n pentominoes of shapes X, Y, Z.
4
1, 0, 0, 0, 0, 6, 6, 6, 2, 10, 86, 118, 166, 152, 372, 1394, 2450, 3866, 4946, 10160, 26380, 50770, 86522, 131632, 251150, 548436, 1075036, 1918294, 3205242, 5953962, 11962044, 23255472, 42565706, 74859582, 138078796, 266506794, 511327170, 947685504, 1713749022
OFFSET
0,6
LINKS
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,13,7,8,1,-10,-14,-20,-8,-7,-38,-33,-2,0,-5,-16,-11).
FORMULA
G.f.: (x^20 +6*x^19 +5*x^18 +7*x^15 +14*x^14 +7*x^13 +4*x^10 +2*x^9 +x^8 -2*x^7 -x^6 -7*x^5 -3*x^4 +1) / (11*x^20 +16*x^19 +5*x^18 +2*x^16 +33*x^15 +38*x^14 +7*x^13 +8*x^12 +20*x^11 +14*x^10 +10*x^9 -x^8 -8*x^7 -7*x^6 -13*x^5 -3*x^4 +1).
EXAMPLE
a(5) = 6:
._________. ._________.
|_. ._._| | | |___. ._|
| |_| |_. | | |_ |_| |
| |_. ._| | | ._| |_. |
| ._|_| |_| (2) |_| |___| | (4)
|_|_______| |_______|_| .
.
a(8) = 2:
._______________.
|_. | |___. ._| |
| | |___. |_|_. |
| |___| |_|_. | |
| ._| |___. | |_| (2)
|_|_______|_|___| .
.
CROSSREFS
Sequence in context: A272619 A172360 A175288 * A153509 A248093 A373021
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Nov 09 2021
STATUS
approved