A341502 Number of matchings in the 3 X n rook graph.

1, 4, 32, 370, 5950, 122984, 3175696, 98815588, 3638940860, 155377163440, 7598445388096, 420034502219864, 26014375783223272, 1788772035008337760, 135644687161742899520, 11268192704027639350384, 1020100484786824631520016, 100126060947226759050509888

Offset: 0

Author

Andrew Howroyd, Feb 21 2021

Keywords

• nonn

Links

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

Crossrefs

Row 3 of A270227.

Cf. A000085, A341848, A341851.

Programs

PARI

\\ here b(n) is A000085.
b(n)={sum(k=0, n\2, n!/((n-2*k)!*2^k*k!))}
a(n)={my(v=vector(n+1, i, b(i-1))); sum(i=0,n, sum(j=0, n-i, sum(k=0, n-i-j, n!/(i!*j!*k!*(n-i-j-k)!)*v[1+n-i-j]*v[1+n-i-k]*v[1+n-j-k] )))}

Formula

a(n) = Sum{i,j,k>=0, i+j+k<=n} n!/(i!*j!*k!*(n-i-j-k)!) * A000085(n-i-j) * A000085(n-i-k) * A000085(n-j-k).