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A247121 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes P, U.

%I A247121 #16 Feb 06 2017 18:34:43
%S A247121 1,2,12,56,248,1184,5472,25376,118208,548864,2550912,11856896,
%T A247121 55098368,256070144,1190065152,5530658816,25703241728,119453057024,
%U A247121 555145224192,2579979739136,11990182412288,55723107221504,258967268524032,1203523043065856,5593246378754048
%N A247121 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes P, U.
%H A247121 Alois P. Heinz, <a href="/A247121/b247121.txt">Table of n, a(n) for n = 0..1000</a>
%H A247121 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A247121 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,20).
%F A247121 G.f.: (4*x^3-1)/(20*x^3+8*x^2+2*x-1).
%e A247121 a(2) = 12:
%e A247121 ._______.      ._______.      ._______.      ._______.
%e A247121 |   |   |      |   ._| |      | ._|   |      | ._|   |
%e A247121 | ._| ._|      |___|   |      | |_____|      | |_____|
%e A247121 |_| |_| |      |   |___|      |___|   |      |___|_. |
%e A247121 |   |   |      | ._|   |      |   |_. |      |   ._| |
%e A247121 |___|___| (*4) |_|_____| (*2) |_____|_| (*4) |___|___| (*2) .
%p A247121 a:= n-> ceil((<<0|1|0>, <0|0|1>, <20|8|2>>^(n-1). <<2, 12, 56>>)[1, 1]):
%p A247121 seq(a(n), n=0..30);
%Y A247121 Cf. A174249, A233427, A247076.
%K A247121 nonn
%O A247121 0,2
%A A247121 _Alois P. Heinz_, Nov 19 2014