A174249 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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.

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

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.

Sequence in context: A247774 A258490 A255953 * A073563 A006658 A221160

Adjacent sequences: A174246 A174247 A174248 * A174250 A174251 A174252

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

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

STATUS

approved