[seqfan] Re: Tatami

zbi74583.boat at orange.zero.jp zbi74583.boat at orange.zero.jp
Tue Apr 26 05:51:00 CEST 2016


    Hi,Seqfans

    The case of 5 x n room, n is odd, number of tiling is represented as follows

    S(n)=S_1(n)+S_5(n)+S_3(n)

    S_1(n)=2*(Sum_{0<=k<=[(n-1)/6]}
((n+3)/4-1/2*k)*((n-1)/4-1/2*k)!/(k!*((n-1)/4-3/2*k)!)
    If n=1 Mod 4 then k is even else k is odd

    S_5(n)=2*(Sum_{0<=k<=[(n-5)/6]}
((n+7)/4-1/2*k)*((n-5)/4-1/2*k)!/(k!*((n-5)/4-3/2*k)!)
    If n=1 Mod 4 then k is even else k is odd

    S_3(n)=2*(Sum_{0<=k<=[(n-3)/6]} 2*((n-3)/4-1/2*k)!/(k!*((n-3)/4-3/2*k)!)
    If n=1 Mod 4 then k is odd  else k is even

    S(n) : 10,8,18,24,32,52
    OFFSET  5

    Numbers computed with the formula and numbers with blute force are the same
    So, it seem to be correct

    Richard
    Could you confirm them and compute more term?



    Yasutoshi




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