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A061552
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Number of 1324-avoiding permutations of length n.
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4
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1, 1, 2, 6, 23, 103, 513, 2762, 15793, 94776, 591950, 3824112, 25431452, 173453058, 1209639642, 8604450011, 62300851632, 458374397312, 3421888118907, 25887131596018, 198244731603623, 1535346218316422, 12015325816028313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| M. H. Albert, M. Elder, A. Rechnitzer, P. Westcott, M. Zabrocki, On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia, arXiv:math.CO/0502504.
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EXAMPLE
| a(4)=23 because all 24 permutations of length 4, except 1324 itself, avoid pattern 1324.
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MAPLE
| count1324 := proc(n::nonnegint) if (n<4) then return n!; fi; if (n=4) then return 23; fi; return nodes([5, 5, 5, 5], n-5) + nodes([5, 3, 5, 5], n-5) + nodes([5, 4, 4, 5], n-5) + nodes([5, 5, 4, 5], n-5) + nodes([4, 3, 4], n-5) + nodes([5, 3, 4, 5], n-5); end:
nodes := proc(p, h) option remember; local i, j, s, l; if (h=0) then return convert(p, `+`); fi; s := 0; for j to nops(p) do l := p[j]+1; for i from 2 to j do l := l, `min`(j+1, p[i]); od; for i from j+1 to p[j] do l := l, p[i-1]+1; od; s := s+nodes([l], h-1); od; return s; end:
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CROSSREFS
| Sequence in context: A004040 A022558 A005802 * A053488 A117106 A137534
Adjacent sequences: A061549 A061550 A061551 * A061553 A061554 A061555
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KEYWORD
| nonn
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AUTHOR
| Darko Marinov (marinov(AT)lcs.mit.edu), May 17 2001
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EXTENSIONS
| More terms from Vince Vatter (vatter(AT)math.rutgers.edu), Feb 26 2005
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