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A201497
Number of permutations that avoid the barred pattern bar{1}43bar{5}2.
0
1, 1, 2, 5, 14, 43, 145, 538, 2194, 9790, 47491, 248706, 1396799, 8363711, 53121000, 356309314, 2514395528, 18606000547, 143956459002, 1161612656187, 9753494344997, 85044912003502, 768659919235828, 7189553986402426, 69486510911410279, 693003419860404514
OFFSET
0,3
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.
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
Agrees with A122993 through n=8 term.
Sequence in context: A137551 A148333 A271270 * A122993 A137552 A137553
KEYWORD
nonn
AUTHOR
David Callan, Dec 02 2011
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)