A349187 Number of tilings of a 5 X n rectangle using n pentominoes of shapes X, Y, Z.

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

Author

Alois P. Heinz, Nov 09 2021

Keywords

• nonn
• easy

Examples

			a(5) = 6:
  ._________.     ._________.
  |_. ._._| |     | |___. ._|
  | |_| |_. |     | |_  |_| |
  | |_. ._| |     | ._| |_. |
  | ._|_| |_| (2) |_| |___| | (4)
  |_|_______|     |_______|_|      .
.
a(8) = 2:
  ._______________.
  |_. | |___. ._| |
  | | |___. |_|_. |
  | |___| |_|_. | |
  | ._| |___. | |_| (2)
  |_|_______|_|___|      .
.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3700
• 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).

Crossrefs

Cf. A174249, A343529.

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).