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A232757
Number of tilings of a 3 X 4n rectangle with 3n tetrominoes of any shape.
2
1, 23, 997, 44855, 2023309, 91286913, 4118731453, 185831471351, 8384460804153, 378295365602127, 17068167803123941, 770092310699262519, 34745508355302417387, 1567669659985973646979, 70731103937531908893003, 3191290354032154992708783, 143986641757115568305530757
OFFSET
0,2
LINKS
S. Butler, J. Ekstrand, S. Osborne, TETRIS Tiling, AMS Spring Central Sectional, Iowa State University, April 27-28 2013
Wikipedia, Tetris
Wikipedia, Tetromino
Index entries for linear recurrences with constant coefficients, signature (60, -755, 3991, -10223, 12960, -8422, 2809, -470, 36, -1).
FORMULA
G.f.: -(x^9 -29*x^8 +291*x^7 -1336*x^6 +2960*x^5 -3174*x^4 +1591*x^3 -372*x^2 +37*x-1) / (x^10 -36*x^9 +470*x^8 -2809*x^7 +8422*x^6 -12960*x^5 +10223*x^4 -3991*x^3 +755*x^2 -60*x+1).
EXAMPLE
a(1) = 23:
._______. ._______. ._______. ._______. ._______. ._______.
| .___| | |_______| | |___. | |_______| | | | | | ._|_. |
|_|_____| | .___| | |_____|_| | |___. | | |___| | | | | |
|_______| |_|_____| |_______| |_____|_| |___|___| |_|___|_|
._______. ._______. ._______. ._______. ._______. ._______.
| ._| | | | .___| | |_. | |___. | | | | | |_______|
| | |___| | |_| | |___| | | | |_| | |___|___| | | |
|_|_____| |___|___| |_____|_| |___|___| |_______| |___|___|
._______. ._______. ._______. ._______. ._______. ._______.
| ._| ._| | |___. | |_. |_. | | .___| | | ._| | | | | |_. |
| |___| | | |_. |_| | |___| | |_| ._| | | | _| | | |_. | |
|_|_____| |___|___| |_____|_| |___|___| |_|_|___| |___|_|_|
._______. ._______. ._______. ._______. ._______.
|_. ._| | | |_. ._| | .___| | | |___. | |_______|
| |_|_. | | ._|_| | |_| |_. | | ._| |_| |_______|
|_____|_| |_|_____| |_____|_| |_|_____| |_______|.
CROSSREFS
Quadrisection of column k=3 of A230031.
Sequence in context: A183523 A233339 A008961 * A139193 A077283 A167244
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Nov 29 2013
STATUS
approved