A352795 Number of ways to tile a 4 X n strip with squares and L-shaped heptominoes with legs of equal length.

1, 1, 1, 1, 5, 11, 19, 29, 55, 113, 223, 409, 747, 1405, 2691, 5109, 9587, 17965, 33851, 63973, 120731, 227365, 428091, 806789, 1521291, 2867861, 5404363, 10183893, 19193547, 36177333, 68186667, 128509269, 242195691, 456468629, 860324843, 1621477013

Offset

0,5

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,4,2,2,2).

Formula

a(n) = a(n-1) + 4*a(n-4) + 2*a(n-5) + 2*a(n-6) + 2*a(n-7).

G.f.: 1/((1 + x)*(1 - 2*x + 2*x^2 - 2*x^3 - 2*x^4 - 2*x^6)). - Stefano Spezia, Apr 04 2022

Example

Here are two such tilings for a 4 X 4 strip. The latter has four rotations thus demonstrating that a(4)=5.
._______.  ._______.
|_|_|_|_|  | |_|_|_|
|_|_|_|_|  | |_|_|_|
|_|_|_|_|  | |_|_|_|
|_|_|_|_|  |_______|

Mathematica

LinearRecurrence[{1, 0, 0, 4, 2, 2, 2}, {1, 1, 1, 1, 5, 11, 19}, 36];

Crossrefs

Cf. A345953.

Sequence in context: A078179 A045451 A338566 * A368898 A326665 A100920

Adjacent sequences: A352792 A352793 A352794 * A352796 A352797 A352798

Keyword

nonn,easy

Author

Drisana Bhatia, Apr 03 2022

Status

approved