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A341502
Number of matchings in the 3 X n rook graph.
3
1, 4, 32, 370, 5950, 122984, 3175696, 98815588, 3638940860, 155377163440, 7598445388096, 420034502219864, 26014375783223272, 1788772035008337760, 135644687161742899520, 11268192704027639350384, 1020100484786824631520016, 100126060947226759050509888
OFFSET
0,2
LINKS
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).
PROG
(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] )))}
CROSSREFS
Row 3 of A270227.
Sequence in context: A051489 A375949 A295257 * A303049 A375946 A369536
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 21 2021
STATUS
approved