A100354 Maximal number of 1432 patterns in a permutation of 1,2,...,n.

0, 0, 0, 1, 4, 10, 20, 40, 70, 112, 168, 252, 360, 495, 661, 881, 1145, 1457, 1824, 2279, 2804, 3404, 4090, 4906, 5824, 6850, 8000, 9330, 10800, 12417, 14208, 16232, 18440, 20840, 23470, 26395, 29554, 32956, 36652, 40712, 45062, 49712, 54728, 60184

Offset

1,5

References

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

Links

Table of n, a(n) for n=1..44.

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, 3), 1 <= k < n)

Example

a(20) = 2279; the 20-permutation with the most copies of 1432 is 1, 5, 4, 3, 2, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6.

Crossrefs

Cf. A061061, A100355, A100356.

Sequence in context: A366646 A038421 A049032 * A352666 A275358 A048008

Adjacent sequences: A100351 A100352 A100353 * A100355 A100356 A100357

Keyword

nonn

Author

Vincent Vatter, Nov 18 2004

Status

approved