[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




More information about the SeqFan mailing list