The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A263885

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A263885

Number of permutations of [n] containing exactly one occurrence of the consecutive pattern 132.
(history; published version)

#14 by Vaclav Kotesovec at Thu Oct 17 18:01:23 EDT 2019

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#13 by Vaclav Kotesovec at Thu Oct 17 17:57:42 EDT 2019

FORMULA

a(n) ~ c * d^n * n! * n, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))) = 0.78397693120354749... and c = 0.679554202696108785... . - Vaclav Kotesovec, Oct 29 2015

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#12 by Vaclav Kotesovec at Thu Oct 29 08:46:14 EDT 2015

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#11 by Vaclav Kotesovec at Thu Oct 29 08:42:51 EDT 2015

MATHEMATICA

Drop[Coefficient[CoefficientList[Series[1/(1 - (Sqrt[Pi/2]*Erfi[(Sqrt[u-1]*x) / Sqrt[2]])/Sqrt[u-1]), {x, 0, 25}], x] * Range[0, 25]!, u], 3] (* Vaclav Kotesovec, Oct 29 2015 *)

#10 by Vaclav Kotesovec at Thu Oct 29 08:26:20 EDT 2015

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InverseErf.html">Inverse Erf</a>

#9 by Vaclav Kotesovec at Thu Oct 29 08:25:23 EDT 2015

FORMULA

a(n) ~ c * d^n * n! * n, where d = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))) = 0.78397693120354749... and c = 0.679554202696108785... . - Vaclav Kotesovec, Oct 29 2015

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editing

#8 by Alois P. Heinz at Wed Oct 28 18:47:55 EDT 2015

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approved

#7 by Alois P. Heinz at Wed Oct 28 18:47:28 EDT 2015

EXAMPLE

a(7) = 2649: 1234576, 1234657, 1234756, ..., 7652431, 7653142, 7654132.

#6 by Alois P. Heinz at Wed Oct 28 18:46:20 EDT 2015

EXAMPLE

a(3) = 1: 132.

a(4) = 8: 1243, 1324, 1423, 1432, 2143, 2431, 3142, 4132.

a(5) = 54: 12354, 12435, 12534, ..., 52431, 53142, 54132.

a(6) = 368: 123465, 123546, 123645, ..., 652431, 653142, 654132.

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#5 by Alois P. Heinz at Wed Oct 28 17:29:56 EDT 2015

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