A100355 Maximal number of 15432 patterns in a permutation of 1,2,...,n.

0, 0, 0, 0, 1, 5, 15, 35, 70, 140, 252, 420, 660, 990, 1485, 2145, 3003, 4095, 5460, 7280, 9520, 12240, 15504, 19381, 24226, 29926, 36576, 44276, 53135, 63761, 75905, 89705, 105305, 122865, 143340, 166272, 191850, 220270, 251755, 287715, 327395, 371043

Offset

1,6

References

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

Links

Table of n, a(n) for n=1..42.

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, 4), 1 <= k < n)

Example

a(24) = 19381; the 24-permutation with the most copies of 15432 is 1, 5, 4, 3, 2, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6.

Crossrefs

Cf. A061061, A100354, A100356.

Sequence in context: A137360 A195760 A195761 * A048032 A019499 A229885

Adjacent sequences: A100352 A100353 A100354 * A100356 A100357 A100358

Keyword

nonn

Author

Vincent Vatter, Nov 18 2004

Status

approved