[seqfan] Tatami
zbi74583.boat at orange.zero.jp
zbi74583.boat at orange.zero.jp
Tue Feb 23 04:58:49 CET 2016
Hi,Seqfans
I computed some Tatami sequences
For tiling n*m room, if both n and m are odd then we need a monomer.
Erickson and Ruskey researched many such kind of tiling
But they computed with no condition of the number of monomer
In order to the traditional method of Tatami tiling we are able to use only
one monomer
So we computed two Tatami tiling of n*m room where both n m are odd
n*n n=2*k+1
S(k) 1,10,10,....
For 0<k S(k)=10
._._._
Fig.1 |_._| | k=1
| |_|_|
|_|_._|
3*n n is odd
S(n) 2,10,18,38,72....
S(n)=S_1(n)+S_3(n)
S_1(n)=
2*(Sum_{0<=k<=[(n-1)/4]} ((n+1)/2-k)*((n-1)/2-k)!/(k!*((n-1)/2-2*k)!))
S_3(n)=
2*(Sum_{0<=k<-[(n-3)/4]} ((n+3)/2-k)*((n-3)/2-k)!/(k!*((n-3)/2-2*k)!))
Where [n] is Floor(n)
My friend who want to be anonymous told me the formula and these terms
I confirmed them
Could anyone confirm it and compute more terms?
Yasutoshi
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