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Search: id:A100354
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| A100354 |
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Maximal number of 1432 patterns in a permutation of 1,2,...,n. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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M. Bona, B. Sagan, V. Vatter, Pattern frequency sequences and internal zeros, Advances in Applied Mathematics 28 (2002), pp. 395-420.
M. Hildebrand, B. Sagan, V. Vatter, Bounding quantities related to the packing density of 1(l+1)l...2, Advances in Applied Mathematics, 33 (2004), pp. 633-653.
W. Stromquist, Packing layered posets into posets, manuscript.
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LINKS
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M. Bona, B. Sagan, V. Vatter, Pattern frequency sequences and internal zeros
M. Hildebrand, B. Sagan, V. Vatter, Bounding quantities related to the packing density of 1(l+1)l...2
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FORMULA
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a(n) = max(a(k) + k*choose(n-k, 3), 1 <= k < n)
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EXAMPLE
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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.
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CROSSREFS
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Cf. A061061, A100355, A100356.
Sequence in context: A164617 A038421 A049032 this_sequence A048008 A048019 A019498
Adjacent sequences: A100351 A100352 A100353 this_sequence A100355 A100356 A100357
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KEYWORD
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nonn
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AUTHOR
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Vince Vatter (vatter(AT)math.rutgers.edu), Nov 18 2004
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