A174249 Number of tilings of a 5 X n rectangle with n pentominoes of any shape.

1, 1, 5, 56, 501, 4006, 27950, 214689, 1696781, 13205354, 101698212, 782267786, 6048166230, 46799177380, 361683136647, 2793722300087, 21583392631817, 166790059833039, 1288885349447958, 9959188643348952, 76953117224941654, 594617039453764617, 4594660583890506956

Offset: 0

Author

Bob Harris (me13013(AT)gmail.com), Mar 13 2010

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Jessica Gonzalez, Illustration for a(2) = 5
• R. S. Harris, Counting Nonomino Tilings and Other Things of that Ilk, G4G9 Gift Exchange book, 2010.
• R. S. Harris, Counting Polyomino Tilings
• Vaclav Kotesovec, G.f. and the recurrence (of order 324)
• Wikipedia, Pentomino
• Index entries for linear recurrences with constant coefficients, order 324.

Crossrefs

Cf. A134438, A174248, A174250, A174251, A174252, A174253, A246902, A278456.

Column k=5 of A233427.

Row sums of A247702, A247703, A247704, A247705, A247706, A247707, A247708, A247709, A247710, A247711, A247712, A247713.

Formula

a(n) ~ c * d^n, where d =

7.727036840800092392128639105511391434436212757335030092041375597587338371937..., c =

0.13364973920881772493778581621701653927538155984099992758656160782495174... (1/d is the root of the denominator, see g.f.). - Vaclav Kotesovec, May 19 2015

Extensions

a(0) prepended, a(11)-a(22) from Alois P. Heinz, Dec 05 2013