A084480 Number of tilings of a 4 X 2n rectangle with L tetrominoes.
1, 2, 10, 42, 182, 790, 3432, 14914, 64814, 281680, 1224182, 5320310, 23122148, 100489226, 436727814, 1898026232, 8248853134, 35849651070, 155803171860, 677123141810, 2942788286798, 12789406189672, 55582969192486, 241564496305670, 1049843265359828
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Nicolas Bělohoubek and Antonín Slavík, L-Tetromino Tilings and Two-Color Integer Compositions, Univ. Karlova (Czechia, 2025). See p. 2.
- Cristopher Moore, Some Polyomino Tilings of the Plane, arXiv:9905012 [math.CO], 1999.
- Index entries for linear recurrences with constant coefficients, signature (4,2,-1,-4,-4,-2).
Programs
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Mathematica
LinearRecurrence[{4, 2, -1, -4, -4, -2}, {1, 2, 10, 42, 182, 790}, 25] (* Jean-François Alcover, Feb 25 2020 *) -
PARI
Vec((1 - 2*x - x^3) / (1 - 4*x - 2*x^2 + x^3 + 4*x^4 + 4*x^5 + 2*x^6) + O(x^30)) \\ Colin Barker, Mar 28 2017
Formula
G.f.: (1-2*z-z^3) / (1-4*z-2*z^2+z^3+4*z^4+4*z^5+2*z^6).
a(n) = 4*a(n-1) + 2*a(n-2) - a(n-3) - 4*a(n-4) - 4*a(n-5) - 2*a(n-6) for n>5. - Colin Barker, Mar 28 2017
Extensions
Inserted a(0)=1 by Alois P. Heinz, May 01 2013