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

Author

Alois P. Heinz, Dec 06 2022

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

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

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).