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Search: id:A117158
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| A117158 |
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Number of permutations avoiding the pattern 1234. |
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+0
2
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| 1, 1, 2, 6, 23, 111, 642, 4326, 33333, 288901, 2782082, 29471046, 340568843, 4263603891, 57482264322, 830335952166, 12793889924553, 209449977967081, 3630626729775362, 66429958806679686, 1279448352687538463
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OFFSET
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0,3
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COMMENT
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a(n) is the number of permutations on [n] that avoid the consecutive pattern 1234. It is the same as the number of permutations which avoid 4321.
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REFERENCES
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Sergi Elizalde, Asymptotic enumeration of permutations avoiding generalized patterns, Adv. Appl. Math. 36 (2006) 138-155.
Sergi Elizalde and Marc Noy, Consecutive patterns in permutations, Adv. Appl. Math. 30 (2003) 110-125.
I. Gessel, Symmetric functions ..., J. Combin. Theory A 53 (1990), 257-285.
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MATHEMATICA
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a[n_]:=Coefficient[Series[2/(Cos[x]-Sin[x]+Exp[ -x]), {x, 0, 30}], x^n]*n!
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CROSSREFS
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Cf. A022558, A049774, A111004, A113228, A113229.
Sequence in context: A113229 A113228 A063255 this_sequence A059513 A132647 A020122
Adjacent sequences: A117155 A117156 A117157 this_sequence A117159 A117160 A117161
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KEYWORD
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nonn
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AUTHOR
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S. R. Finch (Steven.Finch(AT)inria.fr), Apr 26 2006
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