A192096 Maximum number of tatami tilings of any m X m square region with exactly n horizontal dimers and m monomers.

2, 4, 6, 12, 18, 28, 44, 64, 92, 132, 186, 256, 352, 476, 638, 852, 1124, 1472, 1920, 2484, 3196, 4096, 5216, 6612, 8350, 10496, 13140, 16396, 20380, 25244, 31178, 38380, 47104, 57660, 70380, 85684, 104068, 126080, 152396, 183808, 221208, 265664, 318432

Offset

0,1

Comments

A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, Monomer-Dimer Tatami Tilings of Rectangular Regions, Electronic Journal of Combinatorics, 18(1) (2011) P109, 24 pages.

Formula

G.f.: 2 * Product_{k>0} (1 + x^k)^2.

a(n) = 2 * A022567(n).

Example

a(0) = 2 because exactly 2 tilings are possible for 0 horizontal dimers and any m >= 2.  For example, with m = 3:
    _ _ _      _ _ _
   |_| |_|    | |_| |
   | |_| |    |_| |_|
   |_|_|_|    |_|_|_|

Maple

gf:= n-> 2 * mul((1 + x^k)^2, k=1..n):
a:= n-> coeff(series(gf(n), x, n+1), x, n):
seq(a(n), n=0..60);  # Alois P. Heinz, Jul 15 2011

Crossrefs

Cf. A192095, A022567.

Sequence in context: A051683 A215821 A332284 * A181740 A192224 A167777

Adjacent sequences: A192093 A192094 A192095 * A192097 A192098 A192099

Keyword

nonn

Author

Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 15 2011

Status

approved