A358933 Number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, Z.

1, 0, 0, 0, 2, 0, 2, 2, 4, 2, 10, 8, 14, 18, 36, 34, 66, 88, 136, 170, 292, 382, 578, 818, 1244, 1692, 2576, 3676, 5400, 7654, 11412, 16284, 23852, 34448, 50396, 72472, 106046, 153556, 223458, 323430, 471644, 683046, 993958, 1442138, 2097830, 3042314, 4424880

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (0, 0, 5, 2, 10, -4, -7, -35, -26, -34, 13, 43, 94, 115, 51, 30, -124, -99, -276, -52, -131, 182, 128, 298, 189, 71, -30, -118, -118, -96, -56, -8).

Formula

G.f.: (x-1)*(x^2 +x +1)*(4*x^26 +28*x^25 +44*x^24 +29*x^23 +x^22 -36*x^21 -49*x^20 -45*x^19 -61*x^18 +15*x^17 -7*x^16 +60*x^15 +x^14 +59*x^13 -11*x^12 +10*x^11 -37*x^10 -25*x^8 +x^7 -2*x^6 +10*x^5 +4*x^3 -1) / (8*x^32 +56*x^31 +96*x^30 +118*x^29 +118*x^28 +30*x^27 -71*x^26 -189*x^25 -298*x^24 -128*x^23 -182*x^22 +131*x^21 +52*x^20 +276*x^19 +99*x^18 +124*x^17 -30*x^16 -51*x^15 -115*x^14 -94*x^13 -43*x^12 -13*x^11 +34*x^10 +26*x^9 +35*x^8 +7*x^7 +4*x^6 -10*x^5 -2*x^4 -5*x^3 +1).

Example

a(7) = 2:
  ._____________.    ._____________.
  | | ._. | ._. |    | ._. | ._. | |
  | |_| |_|_| |_|    |_| |_|_| |_| |
  |_. |___. |_. |    | ._| .___| ._|
  | |_| | |_| | |    | | |_| | |_| |
  |_____|_____|_|    |_|_____|_____|   .
.

Crossrefs

Cf. A174249, A343529, A349187, A352421, A361250.

Sequence in context: A308212 A181346 A300815 * A002121 A279158 A273166

Adjacent sequences: A358930 A358931 A358932 * A358934 A358935 A358936

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 06 2022

Status

approved