A322497 - OEIS

A322497

Number of tilings of a 4 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.

%I #14 May 02 2022 18:35:34

%S 1,1,5,18,68,233,838,2989,10687,38097,136002,485370,1732377,6182628,

%T 22065919,78752901,281068809,1003130814,3580164896,12777572157,

%U 45603031014,162756761629,580877276331,2073145244569,7399034871398,26407082201462,94246615039341

%N Number of tilings of a 4 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.

%C The shapes of the tiles are:

%C ._.

%C ._. | |

%C ._. | | | |

%C ._. | |_. | |_._. | |_._._.

%C |_| |___| |_____| |_______| .

%H Alois P. Heinz, <a href="/A322497/b322497.txt">Table of n, a(n) for n = 0..1000</a>

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

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,9,17,13,5,-2,-2).

%F G.f.: -(x+1)*(x^3+x-1)/((2*x^2+1)*(x^6+x^5-3*x^4-7*x^3-7*x^2-x+1)).

%t LinearRecurrence[{1,5,9,17,13,5,-2,-2},{1,1,5,18,68,233,838,2989},30] (* _Harvey P. Dale_, May 02 2022 *)

%Y Column k=4 of A322494.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Dec 12 2018