A247268 Number of tilings of a 5 X n rectangle using n pentominoes of shapes Y, U, X.

1, 0, 0, 1, 0, 2, 1, 0, 4, 5, 38, 22, 13, 90, 144, 457, 408, 386, 1267, 2230, 5912, 6481, 7098, 18896, 35433, 79634, 101232, 127501, 288304, 546652, 1113907, 1560356, 2148298, 4408181, 8335234, 15954116, 23827541, 35011426, 67591204, 126376945, 232719926

Offset

0,6

Links

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

Wikipedia, Pentomino

Formula

G.f.: see Maple program.

Example

a(3) = 1, a(5) = 2:
._____.     ._________.   ._________.
| ._. |     |_. .___| |   | |___. ._|
|_| |_|     | |_| |_. |   | ._| |_| |
|_. ._|  ,  | |_. ._| |   | |_. ._| |
| |_| |     | ._|_| |_|   |_| |_|_. |
|_____|     |_|_______|   |_______|_|  .

Maple

gf:= -(x^40 +12*x^39 +36*x^38 -5*x^36 -2*x^35 +12*x^34 +54*x^33 +4*x^32 -21*x^31 -23*x^30 +4*x^29 +20*x^28 +4*x^27 -4*x^25 -7*x^24 -6*x^23 -3*x^22 +33*x^21 -7*x^20 -10*x^19 -12*x^18 -9*x^17 +12*x^16 +16*x^15 +3*x^14 -2*x^13 -2*x^12 -2*x^11 -3*x^10 +5*x^9 -2*x^6 -7*x^5 -x^4 +1) /
(x^43 +12*x^42 +36*x^41 -3*x^40 -29*x^39 -58*x^38 +12*x^37 +67*x^36 +4*x^35 -123*x^34 -99*x^33 +8*x^32 +23*x^31 -145*x^30 -52*x^29 -52*x^28 -35*x^27 -112*x^26 -99*x^25 -28*x^24 -7*x^23 -15*x^22 -99*x^21 -42*x^20 +22*x^19 +36*x^18 +26*x^17 -4*x^16 +6*x^15 +31*x^14 +5*x^13 +11*x^12 +14*x^11 +23*x^10 -5*x^9 -7*x^8 -x^7 +2*x^6 +9*x^5 +x^4 +x^3 -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..60);

Crossrefs

Cf. A174249, A233427, A247124, A247125.

Sequence in context: A269952 A361954 A342500 * A266867 A151852 A300864

Adjacent sequences: A247265 A247266 A247267 * A247269 A247270 A247271

Keyword

nonn

Author

Alois P. Heinz, Nov 30 2014

Status

approved