A341851 Number of maximum matchings in the 3 X n rook graph.

1, 3, 4, 72, 132, 7020, 17280, 1920240, 6022800, 1154366640, 4421511360, 1303028052480, 5906331224640, 2481613890275520, 13003380449579520, 7385997122881977600, 43944212734316294400, 32440254625217626387200, 216088204725662645376000

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Prog

(PARI) 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

Crossrefs

Row n=3 of A341850.

Cf. A341502, A341848.

Sequence in context: A012087 A012194 A318208 * A132414 A041171 A279935

Adjacent sequences: A341848 A341849 A341850 * A341852 A341853 A341854

Keyword

nonn

Author

Andrew Howroyd, Feb 21 2021

Status

approved