login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 14
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.

Sequence in context: A278385 A245626 A307233 * A163535 A288395 A288644

Adjacent sequences:  A233317 A233318 A233319 * A233321 A233322 A233323

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Dec 07 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 4 19:15 EST 2021. Contains 341797 sequences. (Running on oeis4.)