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Search: id:A116844
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| A116844 |
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Number of permutations of length n which avoid the patterns 231, 12345. |
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+0
1
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| 1, 2, 5, 14, 41, 116, 302, 715, 1549, 3106, 5831, 10352, 17525, 28484, 44696, 68021, 100777, 145810, 206569, 287186, 392561, 528452, 701570, 919679, 1191701, 1527826, 1939627, 2440180, 3044189, 3768116
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = number of Dyck n-paths (A000108) with <=4 peaks. So a(n) is the sum of columns 1,2,3,4 in the Narayana triangle A001263. - David Callan (callan(AT)stat.wisc.edu), Jul 03 2006
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LINKS
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Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
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FORMULA
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G.f.: A(x) = -{(x^6-3x^5+13x^4-14x^3+12^2-5x+1)x}/{(x-1)^7}
a(n) = (n^6 - 9n^5 + 43n^4 - 99n^3 + 172n^2 - 108n + 144)/144. - Franklin T. Adams-Watters, Sep 16 2006
Equals A001263 * [1, 1, 1, 1, 0, 0, 0,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 19 2007
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CROSSREFS
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Sequence in context: A007463 A116846 A080558 this_sequence A116851 A038989 A116850
Adjacent sequences: A116841 A116842 A116843 this_sequence A116845 A116846 A116847
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KEYWORD
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nonn,easy
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AUTHOR
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Lara Pudwell (lpudwell(AT)math.rutgers.edu), Feb 26 2006
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