A221958 Number of n X n rook placements avoiding the pattern 102.

1, 2, 7, 31, 159, 916, 5859, 41462, 324539, 2810398, 26897153, 283648795, 3280219609, 41351673884, 564705224247, 8303579891143, 130750660999203, 2194139204726190, 39075773290973877, 735859491383643477, 14606522141527912317, 304753237798452557652

Offset

0,2

Links

Michel Marcus and Vaclav Kotesovec, Table of n, a(n) for n = 0..33, terms a(22)-a(33) from Vaclav Kotesovec, Dec 26 2013

Dan Daly and Lara Pudwell, Pattern avoidance in rook monoids, Special Session on Patterns in Permutations and Words, Joint Mathematics Meetings, 2013.

Prog

(PARI)
combi(n, k, r, d, s) = {if (n-k == 0, return(1); ); if (d == k, p = 1; for (j=2, k, p *= (r[j+1] - r[j] - 1)!; ); p *= (r[2] - 1)! * (n - r[k+1])!; s += p; , for(i = r[d+1]+1, n, r[d+2] = i; s = combi(n, k, r, d+1, s); ); ); return (s); }
r102(n, k) = { if (k == n, return (n!)); s = 0; v = vector(n, i, i-1); s = combi(n, n-k, v, 0, s); s *= binomial(n, k); return (s); }
a(n) = sum(k=0, n, r102(n, k))
\\ Michel Marcus, Feb 21 2013

Crossrefs

Sequence in context: A193320 A030882 A273957 * A221957 A030966 A009132

Adjacent sequences: A221955 A221956 A221957 * A221959 A221960 A221961

Keyword

nonn

Author

N. J. A. Sloane, Feb 04 2013

Extensions

Typo in definition corrected by Vaclav Kotesovec, Feb 04 2013

More terms from Michel Marcus, Feb 21 2013

Status

approved