cp's OEIS Frontend

A232757 Number of tilings of a 3 X 4n rectangle with 3n tetrominoes of any shape.

%I A232757 #21 Jan 27 2025 10:38:31
%S A232757 1,23,997,44855,2023309,91286913,4118731453,185831471351,
%T A232757 8384460804153,378295365602127,17068167803123941,770092310699262519,
%U A232757 34745508355302417387,1567669659985973646979,70731103937531908893003,3191290354032154992708783,143986641757115568305530757
%N A232757 Number of tilings of a 3 X 4n rectangle with 3n tetrominoes of any shape.
%H A232757 Alois P. Heinz, <a href="/A232757/b232757.txt">Table of n, a(n) for n = 0..500</a>
%H A232757 Nicolas Bělohoubek and Antonín Slavík, <a href="https://msekce.karlin.mff.cuni.cz/~slavik/papers/L-tetromino-tilings.pdf">L-Tetromino Tilings and Two-Color Integer Compositions</a>, Univ. Karlova (Czechia, 2025). See p. 10.
%H A232757 S. Butler, J. Ekstrand, S. Osborne, <a href="/A230031/a230031.pdf">TETRIS Tiling</a>, AMS Spring Central Sectional, Iowa State University, April 27-28 2013
%H A232757 R. S. Harris, <a href="http://www.bumblebeagle.org/polyominoes/tilingcounting">Counting Polyomino Tilings</a>
%H A232757 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetris">Tetris</a>
%H A232757 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetromino">Tetromino</a>
%H A232757 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (60, -755, 3991, -10223, 12960, -8422, 2809, -470, 36, -1).
%F A232757 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).
%e A232757 a(1) = 23:
%e A232757 ._______. ._______. ._______. ._______. ._______. ._______.
%e A232757 | .___| | |_______| | |___. | |_______| | |   | | | ._|_. |
%e A232757 |_|_____| | .___| | |_____|_| | |___. | | |___| | | |   | |
%e A232757 |_______| |_|_____| |_______| |_____|_| |___|___| |_|___|_|
%e A232757 ._______. ._______. ._______. ._______. ._______. ._______.
%e A232757 | ._|   | | | .___| |   |_. | |___. | | |   |   | |_______|
%e A232757 | | |___| | |_|   | |___| | | |   |_| | |___|___| |   |   |
%e A232757 |_|_____| |___|___| |_____|_| |___|___| |_______| |___|___|
%e A232757 ._______. ._______. ._______. ._______. ._______. ._______.
%e A232757 | ._| ._| | |___. | |_. |_. | | .___| | | ._| | | | | |_. |
%e A232757 | |___| | | |_. |_| | |___| | |_| ._| | | |  _| | | |_. | |
%e A232757 |_|_____| |___|___| |_____|_| |___|___| |_|_|___| |___|_|_|
%e A232757 ._______. ._______. ._______. ._______. ._______.
%e A232757 |_. ._| | | |_. ._| | .___| | | |___. | |_______|
%e A232757 | |_|_. | | ._|_| | |_| |_. | | ._| |_| |_______|
%e A232757 |_____|_| |_|_____| |_____|_| |_|_____| |_______|.
%Y A232757 Quadrisection of column k=3 of A230031.
%K A232757 nonn,easy
%O A232757 0,2
%A A232757 _Alois P. Heinz_, Nov 29 2013