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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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.

Cf. A000085, A341848, A341851.

Sequence in context: A347021 A051489 A295257 * A303049 A047053 A201594

Adjacent sequences:  A341499 A341500 A341501 * A341503 A341504 A341505

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Feb 21 2021

STATUS

approved

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Last modified October 7 10:36 EDT 2022. Contains 357270 sequences. (Running on oeis4.)