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 A230031 Number A(n,k) of tilings of a k X n rectangle using tetrominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals. 18
 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 4, 0, 4, 0, 1, 1, 0, 0, 23, 23, 0, 0, 1, 1, 0, 9, 0, 117, 0, 9, 0, 1, 1, 1, 0, 0, 454, 454, 0, 0, 1, 1, 1, 0, 25, 0, 2003, 0, 2003, 0, 25, 0, 1, 1, 0, 0, 997, 9157, 0, 0, 9157, 997, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,24 LINKS Alois P. Heinz, Antidiagonals n = 0..20, flattened S. Butler, J. Ekstrand, S. Osborne, TETRIS Tiling, AMS Spring Central Sectional, Iowa State University, April 27-28 2013 R. S. Harris, Counting Polyomino Tilings Wikipedia, Tetris Wikipedia, Tetromino FORMULA A(n,k) = 0 <=> n*k mod 4 > 0. EXAMPLE A(4,2) = A(2,4) = 4:   ._______.  ._______.  ._______.  ._______.   |   |   |  |_______|  | |___. |  | .___| |   |___|___|  |_______|  |_____|_|  |_|_____|. Square array A(n,k) begins:   1, 1,  1,   1,     1,      1,        1,         1,           1, ...   1, 0,  0,   0,     1,      0,        0,         0,           1, ...   1, 0,  1,   0,     4,      0,        9,         0,          25, ...   1, 0,  0,   0,    23,      0,        0,         0,         997, ...   1, 1,  4,  23,   117,    454,     2003,      9157,       40899, ...   1, 0,  0,   0,   454,      0,        0,         0,      800290, ...   1, 0,  9,   0,  2003,      0,   178939,         0,    22483347, ...   1, 0,  0,   0,  9157,      0,        0,         0,   657253434, ...   1, 1, 25, 997, 40899, 800290, 22483347, 657253434, 19077209438, ... CROSSREFS Columns (or rows) include: A000012, A007598, A232757, A174248, A232758, A232684, A232759, A232698, A247113, A232722. Bisection of main diagonal (even part) gives A263425. Cf. A099390, A233320, A233427. Sequence in context: A147986 A147988 A306488 * A019920 A246130 A010675 Adjacent sequences:  A230028 A230029 A230030 * A230032 A230033 A230034 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Nov 29 2013 STATUS approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)