A100356 Maximal number of 165432 patterns in a permutation of 1,2,...,n.

0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 252, 504, 924, 1584, 2574, 4004, 6006, 9009, 13104, 18564, 25704, 34884, 46512, 62016, 81396, 105336, 134596, 170016, 212520, 265650, 328900, 403650, 491400, 593775, 712531, 855037, 1019467, 1208257, 1424017

Offset

1,7

References

W. Stromquist, Packing layered posets into posets, manuscript.

Links

Table of n, a(n) for n=1..39.

M. Bona, B. Sagan, and V. Vatter, Pattern frequency sequences and internal zeros, Advances in Applied Mathematics 28 (2002), pp. 395-420.

M. Hildebrand, B. Sagan, and V. Vatter, Bounding quantities related to the packing density of 1(l+1)l...2, Advances in Applied Mathematics, 33 (2004), pp. 633-653.

Formula

a(n) = max(a(k) + k*choose(n-k, 5), 1 <= k < n)

Example

a(12) = 502; the 12-permutation with the most copies of 165432 is 2, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3.

Crossrefs

Cf. A061061, A100354, A100355.

Sequence in context: A290993 A275936 A019500 * A229886 A243740 A369794

Adjacent sequences: A100353 A100354 A100355 * A100357 A100358 A100359

Keyword

nonn

Author

Vincent Vatter, Nov 18 2004

Status

approved