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
Keywords
Examples
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.
References
- W. Stromquist, Packing layered posets into posets, manuscript.
Links
- 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)