A174249 - OEIS

%I #41 Apr 27 2022 10:38:56

%S 1,1,5,56,501,4006,27950,214689,1696781,13205354,101698212,782267786,

%T 6048166230,46799177380,361683136647,2793722300087,21583392631817,

%U 166790059833039,1288885349447958,9959188643348952,76953117224941654,594617039453764617,4594660583890506956

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

%H Alois P. Heinz, <a href="/A174249/b174249.txt">Table of n, a(n) for n = 0..1000</a>

%H Jessica Gonzalez, <a href="/A174249/a174249.png">Illustration for a(2) = 5</a>

%H R. S. Harris, <a href="http://www.bumblebeagle.org/polyominoes/tilingcounting/counting_9x9_tilings.pdf">Counting Nonomino Tilings and Other Things of that Ilk</a>, G4G9 Gift Exchange book, 2010.

%H R. S. Harris, <a href="http://www.bumblebeagle.org/polyominoes/tilingcounting">Counting Polyomino Tilings</a>

%H Vaclav Kotesovec, <a href="/A174249/a174249.txt">G.f. and the recurrence (of order 324)</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>

%H <a href="/index/Rec#order_324">Index entries for linear recurrences with constant coefficients</a>, order 324.

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

%F 7.727036840800092392128639105511391434436212757335030092041375597587338371937..., c =

%F 0.13364973920881772493778581621701653927538155984099992758656160782495174... (1/d is the root of the denominator, see g.f.). - _Vaclav Kotesovec_, May 19 2015

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

%Y Column k=5 of A233427.

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

%K nonn,easy

%O 0,3

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

%E a(0) prepended, a(11)-a(22) from _Alois P. Heinz_, Dec 05 2013