This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A192096 #30 Jan 01 2023 09:47:13
%S A192096 2,4,6,12,18,28,44,64,92,132,186,256,352,476,638,852,1124,1472,1920,
%T A192096 2484,3196,4096,5216,6612,8350,10496,13140,16396,20380,25244,31178,
%U A192096 38380,47104,57660,70380,85684,104068,126080,152396,183808,221208,265664,318432
%N A192096 Maximum number of tatami tilings of any m X m square region with exactly n horizontal dimers and m monomers.
%C A192096 A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point.
%H A192096 Alois P. Heinz, <a href="/A192096/b192096.txt">Table of n, a(n) for n = 0..1000</a>
%H A192096 A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, <a href="https://doi.org/10.37236/596">Monomer-Dimer Tatami Tilings of Rectangular Regions</a>, Electronic Journal of Combinatorics, 18(1) (2011) P109, 24 pages.
%F A192096 G.f.: 2 * Product_{k>0} (1 + x^k)^2.
%F A192096 a(n) = 2 * A022567(n).
%e A192096 a(0) = 2 because exactly 2 tilings are possible for 0 horizontal dimers and any m >= 2. For example, with m = 3:
%e A192096 _ _ _ _ _ _
%e A192096 |_| |_| | |_| |
%e A192096 | |_| | |_| |_|
%e A192096 |_|_|_| |_|_|_|
%p A192096 gf:= n-> 2 * mul((1 + x^k)^2, k=1..n):
%p A192096 a:= n-> coeff(series(gf(n), x, n+1), x, n):
%p A192096 seq(a(n), n=0..60); # _Alois P. Heinz_, Jul 15 2011
%Y A192096 Cf. A192095, A022567.
%K A192096 nonn
%O A192096 0,1
%A A192096 _Frank Ruskey_ and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 15 2011