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

0,6

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).

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

Cf. A174249, A343529.

Sequence in context: A272619 A172360 A175288 * A153509 A248093 A373021

Adjacent sequences: A349184 A349185 A349186 * A349188 A349189 A349190

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 09 2021

Status

approved