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

0,3

Comments

The shapes of the tiles are:

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

|_| |___| |_____| |_______| .

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).

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)).

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 *)

Crossrefs

Column k=4 of A322494.

Sequence in context: A166677 A318062 A158879 * A279488 A199843 A109438

Adjacent sequences: A322494 A322495 A322496 * A322498 A322499 A322500

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 12 2018

Status

approved