A345448 Number of tilings of a 2 X n rectangle with dominoes and long L-shaped 4-minoes.

1, 1, 2, 7, 15, 32, 79, 185, 422, 987, 2307, 5352, 12451, 29005, 67478, 156991, 365391, 850304, 1978615, 4604465, 10715078, 24934611, 58024779, 135028632, 314222011, 731218981, 1701605078, 3959769367, 9214694391, 21443322032, 49900304047, 116121942377

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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

Formula

a(n) = a(n-1) + a(n-2) + 4*a(n-3) + 2*a(n-4).

Sum_{j=0..n} a(n) = (1/7)(a(n+4) - a(n+2) - 5*a(n+1) - 1).

G.f.: 1/(1 - x - x^2 - 4*x^3 - 2*x^4). - Stefano Spezia, Jun 19 2021

Example

For n = 3 the a(3)=7 tilings are:
._____.  ._____.  ._____.  ._____.
| |___|  |___| |  |  ___|  |___  |
|_____|  |_____|  |_|___|  |___|_|
._____.  ._____.  ._____.
|___| |  | |___|  | | | |
|___|_|  |_|___|  |_|_|_|

Mathematica

LinearRecurrence[{1, 1, 4, 2}, {1, 1, 2, 7}, 40]

Crossrefs

Cf. A052980.

Sequence in context: A343531 A095091 A131412 * A209633 A216633 A295145

Adjacent sequences: A345445 A345446 A345447 * A345449 A345450 A345451

Keyword

nonn,easy

Author

Greg Dresden and Yiwen Zhang, Jun 19 2021

Status

approved