OFFSET
0,3
COMMENTS
a(n) is the number of permutations of [n] that avoid the barred pattern bar{1}43bar{5}2. A permutation p avoids bar{1}43bar{5}2 if each instance of a not-necessarily-consecutive 432 pattern in p is part of a 14352 pattern in p.
LINKS
David Callan, A permutation pattern that illustrates the strong law of small numbers, arXiv:1111.6297
Lara Pudwell, Enumeration Schemes for Permutations Avoiding Barred Patterns, Electronic J. Combinatorics, Vol. 17 (1), 2010, R29, 27pp.
EXAMPLE
14352 is an avoider because the 432 has the required "1" and "5" in appropriate position, but 512463 is not because 543 is a 432 pattern with no available "1".
MATHEMATICA
Clear[a];
a[0] = a[1] = 1;
a[n_] /; n >= 2 := BellB[n - 1] + 1 + 2^(n - 2) - n +
Sum[(Sum[Binomial[n - 4 - a + j - i, j - i] (i + 2)^b, {i, 0, j}] -
Binomial[n - 3 - a + j, j])*StirlingS2[a - b, j], {a, 0,
n - 3}, {b, 0, a - 1}, {j, 0, a - b}] +
Sum[Binomial[j + a + 1, j + 1] StirlingS2[n - 2 - a, j], {a, 0,
n - 2}, {j, 0, n - 2 - a}];
Table[a[n], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
David Callan, Dec 02 2011
STATUS
approved