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A061061
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Maximal number of 132 patterns in a permutation of 1,2,...,n.
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3
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0, 0, 1, 3, 6, 12, 20, 31, 46, 64, 87, 115, 147, 186, 231, 282, 342, 408, 482, 566, 657, 759, 871, 991, 1126, 1270, 1424, 1594, 1774, 1968, 2177, 2397, 2635, 2887, 3151, 3436, 3735, 4050, 4386, 4736, 5106, 5496, 5901, 6330, 6778, 7244, 7737, 8247, 8778
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| W. Stromquist, Packing layered posets into posets, manuscript.
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LINKS
| Miklos Bona, Bruce E. Sagan and Vincent R. Vatter, Pattern frequency sequences and internal zeros
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FORMULA
| a(n) = max(a(k) + k*C(n-k, 2): 1 <= k < n)
a(n+1)/a(n)=1+3/n+O(1/n^2). n^2*(a(n+1)/a(n)-1-3/n) is bounded but there is no limit; limit n-->infinity a(n)/n^3 = C = 0.0773... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 25 2003
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EXAMPLE
| a(8) = 31; the permutation of 1..8 containing the maximum number of 132 patterns is 13287654.
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CROSSREFS
| Sequence in context: A160732 A066140 A200067 * A001975 A096220 A034333
Adjacent sequences: A061058 A061059 A061060 * A061062 A061063 A061064
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KEYWORD
| easy,nonn
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AUTHOR
| Michael H. Albert (malbert(AT)cs.otago.ac.nz), May 27 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 03 2001
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