A217830 -id:A217830 - cp's OEIS frontend

A217799 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 2, 16, 168, 2112, 30030, 466752, 7759752, 135980416

Offset: 0

N. J. A. Sloane, Oct 12 2012

Probably the same as A123555 for n>0. - R. J. Mathar, Nov 22 2023

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(6)-a(8) from Lars Blomberg, Jan 23 2018

A217800 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 2, 12, 110, 1274, 17136, 255816, 4124406, 70549050, 1264752060, 23555382240, 452806924752, 8939481277552, 180551099694400, 3719061442253520, 77933728043586630, 1658001861319441050, 35749633305661575300, 780123576993991461000, 17208112644166765652100

Offset: 0

N. J. A. Sloane, Oct 12 2012

nonn

1 together with A007724. - Omar E. Pol, Aug 22 2016

K. Gorska and K. A. Penson, Multidimensional Catalan and related numbers as Hausdorff moments, arXiv preprint arXiv:1304.6008 [math.CO], 2013.
J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A007724, A181197, A217799-A217830, A005789, A006480, A007724.

[Factorial(3*n+3)/((4*(n+1)^2-1)*Factorial((n+1))^2*Factorial(n+ 2)): n in [0..20]]; // Vincenzo Librandi, Aug 30 2014

a := n -> (-1)^n*hypergeom([-2-2*n, -2*n, -2*n-1], [2, 3], 1):
seq(round(evalf(a(n), 32)), n=0..20); # Peter Luschny, Aug 29 2014

Table[(3 n + 3)!/((4 (n + 1)^2 - 1) ((n + 1)!)^2 (n + 2)!), {n, 0, 20}] (* Vincenzo Librandi, Aug 30 2014 *)
Table[(-1)^n HypergeometricPFQ[{-2 - 2 n, -2 n, -2 n - 1}, {2, 3}, 1], {n, 0, 20}] (* Michael De Vlieger, Aug 22 2016 *)

a(n) = (3*n+3)!/((4*(n+1)^2-1)*((n+1)!)^2*(n+2)!); \\ Michel Marcus, Aug 10 2014

From Karol A. Penson, Aug 10 2014: (Start)
O.g.f.(in Maple notation): hypergeom([1/2, 1, 4/3, 5/3], [2, 5/2, 3], 27*z);a(n) ~ (1/93312)*sqrt(3)*27^n*(314928*n^4-1644624*n^3+5545260*n^2 -15387660*n+38310503)/(Pi*n^8), for n -> infinity.
Representation of a(n) as the n-th power moment of a positive function on the segment [0,27]:
a(n) = int(x^n*W(x),x=0..27),n=0,1,2..., where
W(x) = 1/(Pi*sqrt(x))+sqrt(x)/Pi-(9/20)*sqrt(3)*2^(1/3)* hypergeom([-2/3, -1/6, 1/3], [2/3, 11/6], (1/27)*x)*x^(1/3)/ (sqrt(Pi)*Gamma(5/6)*Gamma(2/3))-(27/56)*2^(2/3)*Gamma(5/6) *Gamma(2/3)*hypergeom([-1/3, 1/6, 2/3], [4/3, 13/6], (1/27)*x)* x^(2/3)/Pi^(5/2).
W(x) for x->0 has the singularity 1/sqrt(x), W(27)=0.
This is the solution of the Hausdorff moment problem and is unique.
a(n) = (1/2)*(n+3)!/((4*(n+1)^2-1)*(n+1)!)*A005789(n), where A005789(n) are the three-dimensional Catalan numbers (see the Gorska and Penson link).(End)
a(n) = A006480(n+1)/((2+n)*(1+2*n)*(3+2*n)). - Peter Luschny, Aug 15 2014
a(n) = (-1)^n*hypergeom([-2-2*n,-2*n,-2*n-1],[2,3],1). - Peter Luschny, Aug 29 2014
(2*n+3)*(n+2)*(n+1)*a(n) -3*(3*n+2)*(2*n-1)*(3*n+1)*a(n-1)=0. - R. J. Mathar, Jun 14 2016
a(n) ~ 3^(3*n + 7/2) / (8*Pi*n^4). - Vaclav Kotesovec, Jun 09 2019

More terms from Alois P. Heinz, Aug 22 2016

Merged with A241958 by R. J. Mathar, Jul 07 2023

A217823 Number of permutations of length 3n with descent set {3, 6, ...} that avoid a certain pattern of length 4 or 5 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 1, 9, 153, 3579, 101630, 3288871

Offset: 0

N. J. A. Sloane, Oct 13 2012

Is this the same sequence as A361190?

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830, A361190.

a(5)-a(6) from Lars Blomberg, Mar 09 2018

a(0)=1 prepended by Alois P. Heinz, Jul 31 2023

A217801 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 2, 12, 106, 1138, 13734, 179192, 2471958, 35557668

Offset: 0

N. J. A. Sloane, Oct 12 2012

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(6)-a(8) from Lars Blomberg, Jan 23 2018

A217802 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 2, 12, 110, 1285, 17653, 272832, 4615282, 83898083

Offset: 0

N. J. A. Sloane, Oct 12 2012

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(6)-a(8) from Lars Blomberg, Jan 23 2018

A217803 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 2, 12, 108, 1202, 15234, 210696, 3102296, 47875884

Offset: 0

N. J. A. Sloane, Oct 12 2012

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(6)-a(8) from Lars Blomberg, Jan 23 2018

A217804 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 2, 16, 168, 2072, 28298, 414472, 6387436, 102316000

Offset: 0

N. J. A. Sloane, Oct 12 2012

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(6)-a(8) from Lars Blomberg, Jan 23 2018

A217805 Number of alternating permutations on 2n letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 5, 42, 444, 5337, 69657, 962939, 13890083, 207042035

Offset: 1

N. J. A. Sloane, Oct 12 2012

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(7)-a(9) from Lars Blomberg, Feb 17 2018

A217806 Number of alternating permutations on 2n letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 4, 28, 260, 2844, 34564, 451868, 6231556, 89510428

Offset: 1

N. J. A. Sloane, Oct 12 2012

J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(7)-a(9) from Lars Blomberg, Feb 17 2018

A217807 Number of alternating permutations on 2n letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Original entry on oeis.org

1, 4, 29, 292, 3620, 51866, 827415, 14350467, 266218320

Offset: 1

N. J. A. Sloane, Oct 12 2012

Andrew R. Conway, Anthony J. Guttmann, Paul Zinn-Justin, 1324-avoiding permutations revisited arXiv:1709.01248 [math.CO], 2017.
J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.

Cf. A181197, A217799-A217830.

a(7)-a(9) from Lars Blomberg, Feb 17 2018

cp's OEIS Frontend

A217799 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A217800 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

Extensions

A217823 Number of permutations of length 3n with descent set {3, 6, ...} that avoid a certain pattern of length 4 or 5 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A217801 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions

A217802 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions

A217803 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions

A217804 Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions

A217805 Number of alternating permutations on 2n letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions

A217806 Number of alternating permutations on 2n letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions

A217807 Number of alternating permutations on 2n letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).

Views

Author

Keywords

Links

Crossrefs

Extensions