The number of ways of cutting a 4 by n (colorless) checkerboard into two con\
    gruent connected pieces is the coefficient of x^n in the Maclaurin expan\
    sion of the following rational function

                 8      7      6      5      4      3      2
           x (2 x  - 4 x  + 8 x  - 7 x  + 3 x  + 2 x  - 5 x  + x + 1)
           ----------------------------------------------------------
                           2   4      2        4      2
                    (x - 1)  (x  + 3 x  - 1) (x  + 2 x  - 1)



                             and in Maple notation



x*(2*x^8-4*x^7+8*x^6-7*x^5+3*x^4+2*x^3-5*x^2+x+1)/(x-1)^2/(x^4+3*x^2-1)/(x^4+2*
x^2-1)


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