A322497 Number of tilings of a 4 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.

1, 1, 5, 18, 68, 233, 838, 2989, 10687, 38097, 136002, 485370, 1732377, 6182628, 22065919, 78752901, 281068809, 1003130814, 3580164896, 12777572157, 45603031014, 162756761629, 580877276331, 2073145244569, 7399034871398, 26407082201462, 94246615039341

Offset: 0

Author

Alois P. Heinz, Dec 12 2018

Keywords

• nonn
• easy

Comments

The shapes of the tiles are:

._.

._. | |

._. | | | |

.. | |. | |.. | |.._.

|| |__| |___| |_____| .

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Polyomino
• Index entries for linear recurrences with constant coefficients, signature (1,5,9,17,13,5,-2,-2).

Crossrefs

Column k=4 of A322494.

Programs

Mathematica

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

Formula

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)).