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A352789 Number of ways to tile a 3 X n strip with squares and P-shaped heptominoes. 0
1, 1, 1, 9, 17, 27, 101, 239, 473, 1315, 3281, 7267, 18265, 45459, 106225, 258907, 637113, 1523443, 3685617, 8994971, 21700329, 52459491, 127466145, 308440011, 746105881, 1809235699, 4381674769, 10605454107, 25696219721, 62241829635, 150703933889, 365037041195 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n) is also the number of ways to tile a 1 X n strip with squares, eight colors of trominoes, and 2 colors of pentominoes.
LINKS
FORMULA
a(n) = a(n-1) + 8*a(n-3) + 2*a(n-5).
G.f.: 1/(1 - x - 8*x^3 - 2*x^5). - Stefano Spezia, Apr 03 2022
EXAMPLE
The a(3) = 9 solutions are as follows:
_____ _____ _____
|_|_|_| | |_| |_| |
|_|_|_| | |_| |_| |
|_|_|_| |_____| |_____|
_____ _____ _____
|_ | | _| | |_|_|
|_| | | |_| | |
|_|___| |___|_| |_____|
_____ _____ _____
|_|_| | | | | |
| | |_ _ | | _ _|
|_____| |_|_|_| |_|_|_|
MATHEMATICA
LinearRecurrence[{1, 0, 8, 0, 2}, {1, 1, 1, 9, 17}, 34];
CROSSREFS
Sequence in context: A235361 A109333 A081030 * A285009 A228260 A147459
KEYWORD
nonn,easy
AUTHOR
Drisana Bhatia, Apr 03 2022
STATUS
approved

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Last modified April 18 03:01 EDT 2024. Contains 371767 sequences. (Running on oeis4.)