A345953 Number of ways to tile a 2 X n strip with squares and P-shaped pentominos.

1, 1, 1, 5, 9, 15, 37, 75, 145, 311, 641, 1295, 2689, 5543, 11345, 23383, 48145, 98903, 203521, 418791, 861169, 1771543, 3644513, 7496231, 15419985, 31720375, 65248385, 134217351, 276091313, 567924823, 1168234977, 2403096999, 4943230993, 10168353527, 20916591169

Offset

0,4

Comments

a(n) is also the number of ways to tile a 1 X n strip with squares, four colors of trominos, and 2 colors of pentominos.

Links

Table of n, a(n) for n=0..34.

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

Formula

a(n) = a(n-1) + 4*a(n-3) + 2*a(n-5).

Sum_{k=0..n} a(k) = (a(n+5) - 4*a(n+2) - 4*a(n+1) - 1)/6.

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

Example

Here is a demonstration that a(3) = 5.
._____.  ._____.  ._____.  ._____.  ._____.
|_|_|_|  |   |_|  |_|   |  |_    |  |    _|
|_|_|_|  |_____|  |_____|  |_|___|  |___|_|

Mathematica

LinearRecurrence[{1, 0, 4, 0, 2}, {1, 1, 1, 5, 9}, 40];

Crossrefs

Sequence in context: A210289 A062516 A249331 * A075133 A351826 A066081

Adjacent sequences: A345950 A345951 A345952 * A345954 A345955 A345956

Keyword

nonn,easy

Author

Drisana Bhatia and Greg Dresden, Jun 29 2021

Status

approved