A269958 -id:A269958

Search: a269958 -id:a269958

Displaying 1-1 of 1 result found.

page 1

A233320

Number A(n,k) of tilings of a k X n rectangle using trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.

+10
17

1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 3, 3, 0, 1, 1, 0, 0, 10, 0, 0, 1, 1, 1, 0, 23, 23, 0, 1, 1, 1, 0, 11, 62, 0, 62, 11, 0, 1, 1, 0, 0, 170, 0, 0, 170, 0, 0, 1, 1, 1, 0, 441, 939, 0, 939, 441, 0, 1, 1, 1, 0, 41, 1173, 0, 8342, 8342, 0, 1173, 41, 0, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,18

COMMENTS

Every row and column satisfies a linear recurrence. - Peter Kagey, Jul 17 2019

LINKS

Alois P. Heinz, Antidiagonals n = 0..28, flattened

Wikipedia, Tromino

FORMULA

A(n,k) = 0 <=> n*k mod 3 > 0.

EXAMPLE

Square array A(n,k) begins:

1, 1, 1, 1, 1, 1, 1, ...

1, 0, 0, 1, 0, 0, 1, ...

1, 0, 0, 3, 0, 0, 11, ...

1, 1, 3, 10, 23, 62, 170, ...

1, 0, 0, 23, 0, 0, 939, ...

1, 0, 0, 62, 0, 0, 8342, ...

1, 1, 11, 170, 939, 8342, 80092, ...

1, 0, 0, 441, 0, 0, 614581, ...

1, 0, 0, 1173, 0, 0, 5271923, ...

CROSSREFS

Columns (or rows) include: A000012, A001835, A134438, A233339, A233340, A233290, A233343, A269958, A215826, A269959, A269664.

Cf. A099390, A230031, A233427, A270061, A364457.

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Dec 07 2013

STATUS

approved

page 1

Search completed in 0.005 seconds