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A247076 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shape P.

%I A247076 #22 May 29 2018 09:52:25
%S A247076 1,2,6,20,62,194,612,1922,6038,18980,59646,187442,589076,1851266,
%T A247076 5817894,18283700,57459518,180575906,567489348,1783428098,5604714422,
%U A247076 17613731780,55354032894,173959101458,546694927604,1718078222594,5399341807686,16968314698580
%N A247076 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shape P.
%H A247076 Alois P. Heinz, <a href="/A247076/b247076.txt">Table of n, a(n) for n = 0..1000</a>
%H A247076 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A247076 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,5).
%F A247076 G.f.: (x-1)*(x^2+x+1)/(5*x^3+2*x^2+2*x-1).
%F A247076 a(n) = 2*a(n-1)+2*a(n-2)+5*a(n-3) for n>3, a(0)=1; a(1)=2, a(2)=6, a(3)=20.
%e A247076 a(2) = 6:
%e A247076 ._______. ._______. ._______. ._______. ._______. ._______.
%e A247076 |   |   | |   |   | |   |   | |   |   | |   ._| | | |_.   |
%e A247076 | ._| ._| |_. |_. | | ._|_. | |_. | ._| |___|   | |   |___|
%e A247076 |_| |_| | | |_| |_| |_| | |_| | |_|_| | |   |___| |___|   |
%e A247076 |   |   | |   |   | |   |   | |   |   | | ._|   | |   |_. |
%e A247076 |___|___| |___|___| |___|___| |___|___| |_|_____| |_____|_| .
%p A247076 a:= proc(n) option remember; `if`(n<4, [1, 2, 6, 20][n+1],
%p A247076        2*a(n-1) +2*a(n-2) +5*a(n-3))
%p A247076     end:
%p A247076 seq(a(n), n=0..40);
%t A247076 Join[{1}, LinearRecurrence[{2, 2, 5}, {2, 6, 20}, 40]] (* _Jean-François Alcover_, May 29 2018 *)
%Y A247076 Even bisection of main diagonal of A247706.
%Y A247076 Cf. A174249, A233427, A247121.
%K A247076 nonn
%O A247076 0,2
%A A247076 _Alois P. Heinz_, Nov 17 2014