A341848
Number of maximal matchings in the 3 X n rook graph.
Original entry on oeis.org
1, 3, 10, 84, 852, 11580, 197640, 4314240, 100855440, 3342895920, 98070406560, 4652556511680, 163444377096000, 10568979882901440, 431650452829115520, 36599310178253222400, 1702185892636880851200, 183500657952824967955200, 9569677207227878912371200
Offset: 0
A341851
Number of maximum matchings in the 3 X n rook graph.
Original entry on oeis.org
1, 3, 4, 72, 132, 7020, 17280, 1920240, 6022800, 1154366640, 4421511360, 1303028052480, 5906331224640, 2481613890275520, 13003380449579520, 7385997122881977600, 43944212734316294400, 32440254625217626387200, 216088204725662645376000
Offset: 0
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a(n)={my(v=vector((n+1)\2+1, i, i--; (2*i)!/(2^i*i!))); if(n%2,3,1)*sum(i=0, n\2, sum(j=0, n\2, sum(k=abs(i-j), min(i+j, n-i-j), n!/((i+k-j)!*(i+j-k)!*(n-i-j-k)!*(j+k-i)!)*v[1+(n+1)\2-i]*v[1+j]*v[1+k] )))} \\ Andrew Howroyd, Mar 14 2021
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