A220860 Triangle read by rows related to enumeration of permutations avoiding certain patterns.

1, 1, 1, 1, 4, 1, 1, 10, 9, 1, 20, 41, 6, 1, 35, 133, 61, 2, 1, 56, 350, 336, 49, 1, 84, 798, 1336, 465, 20, 1, 120, 1638, 4300, 2789, 380, 4, 1, 165, 3102, 11902, 12577, 3581, 192, 1, 220, 5511, 29392, 46487, 22924, 3025, 56

Offset

1,5

Comments

See Barnabei et al. (2012) for precise definition.

Links

Table of n, a(n) for n=1..51.

M. Barnabei, F. Bonetti and M. Silimbani, Two permutation classes related to the Bubble Sort operator, Electronic Journal of Combinatorics 19(3) (2012), #P25. See Theorem 6.

Example

Triangle begins:
1
1 1
1 4   1
1 10  9
1 20  41   6
1 35  133  61   2
1 56  350  336  49
1 84  798  1336 465  20
1 120 1638 4300 2789 380 4
...

Prog

(PARI) rows(nn) = {my(pol = Pol((1 - 3*x + 3*x^2 - 3*x^2*y - x^3 + 2*x^3*y - x^3*y^2)/(1 - 4*x + 6*x^2 - 4*x^2*y - 4*x^3 + 6*x^3*y - 2*x^3*y^2 + x^4 - 2*x^4*y + x^4*y^2) + O(x^nn))); for (i=1, poldegree(pol, x), ypol = polcoeff(pol, i, x); for (j=0, poldegree(ypol, y), print1(polcoeff(ypol, j, y), ", "); ); print(); ); } \\ Michel Marcus, Jul 23 2014

Crossrefs

Cf. A000292 (second column).

Sequence in context: A361731 A109955 A214398 * A174043 A319029 A175124

Adjacent sequences: A220857 A220858 A220859 * A220861 A220862 A220863

Keyword

nonn,tabf

Author

N. J. A. Sloane, Dec 25 2012

Extensions

More terms from Michel Marcus, Jul 23 2014

Keyword set to tabf by Michel Marcus, Jul 23 2014

Status

approved