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Search: id:A117226
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| A117226 |
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Number of permutations avoiding the pattern 1243. |
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+0
1
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| 1, 1, 2, 6, 23, 110, 630, 4204, 32054, 274914, 2619692, 27459344, 313990182, 3889585408, 51888955808, 741668212080, 11307669002720, 183174676857608, 3141820432768752, 56882461258572976, 1084056190235653304
(list; graph; listen)
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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 1243. It is the same as the number of permutations which avoid 3421, 4312 or 2134.
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REFERENCES
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Sergi Elizalde and Marc Noy, Consecutive patterns in permutations, Adv. Appl. Math. 30 (2003) 110-125.
Sergi Elizalde, Asymptotic enumeration of permutations avoiding generalized patterns, Adv. Appl. Math. 36 (2006) 138-155.
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MATHEMATICA
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A[x_]:=Integrate[AiryAi[ -t], {t, 0, x}]; B[x_]:=Integrate[AiryBi[ -t], {t, 0, x}] c:=-3^(2/3)*Gamma[2/3]/2; d:=-3^(1/6)*Gamma[2/3]/2 a[n_]:=Coefficient[Series[1/(c*A[x]+d*B[x]+1), {x, 0, 30}], x^n]*n!
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CROSSREFS
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Cf. A049774, A111004, A113228, A113229.
Sequence in context: A112501 A093345 A002136 this_sequence A117156 A113229 A113228
Adjacent sequences: A117223 A117224 A117225 this_sequence A117227 A117228 A117229
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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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