cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

N. J. A. Sloane, Oct 12 2012

Keywords

Comments

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

Crossrefs

Extensions

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

A011553 Number of standard Young tableaux of type (n,n,n) whose (2,1) entry is odd.

Original entry on oeis.org

0, 2, 16, 182, 2400, 35310, 562848, 9540674, 169777504, 3142665968, 60099912320, 1181283863632, 23767586624960, 487947659276790, 10195163202404160, 216335108170636650, 4653803620322450880, 101343766487960918460, 2231268469684932939360, 49614581272087698764820
Offset: 1

Views

Author

giambruno(AT)ipamat.math.unipa.it

Keywords

Examples

			a(2) = 2 because the standard Young tableaux of type (2,2,2) whose (2,1) entry is odd are:
+---+   +---+
|1 2|   |1 2|
|3 5|   |3 4|
|4 6|   |5 6|
+---+   +---+  - _Alois P. Heinz_, Feb 28 2012
		

References

  • For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.

Crossrefs

Cf. A123555.

Formula

a(n) ~ 3^(3*n+7/2) / (64*Pi*n^4). - Vaclav Kotesovec, Sep 06 2014
Conjecture D-finite with recurrence 6*(n+2)*(n+1)^2*a(n) -(n+1)*(164*n^2-179*n+51) *a(n-1) +(46*n^3-609*n^2+812*n+12) *a(n-2) +12*(3*n-4) *(2*n-5) *(3*n-5)*a(n-3)=0. - R. J. Mathar, Nov 22 2023

Extensions

Definition corrected by Amitai Regev (amitai.regev(AT)weizmann.ac.il), Nov 15 2006
More terms and offset corrected by Alois P. Heinz, Feb 28 2012

A123691 a(n) = number of standard Young tableaux of type (n,n-1,n-1).

Original entry on oeis.org

1, 3, 21, 210, 2574, 36036, 554268, 9145422, 159352050, 2900207310, 54698315490, 1062710129520, 21172455657360, 431010704453400, 8939669081780520, 188478023140872630, 4031562420682009290, 87350519114776867950, 1914486941500560677250, 42397183540866961907100
Offset: 1

Views

Author

Robert G. Wilson v, Nov 15 2006

Keywords

Crossrefs

Cf. A005789, A123555, subdiagonal of A065077.

Programs

  • Maple
    a:= n-> 6 *(3*n-2)! / (n! *(n-1)! *(n+2)!):
    seq(a(n), n=1..25); # Alois P. Heinz, Apr 11 2012
  • Mathematica
    (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@{n, n - 1, n - 1}, {n, 18}]

Formula

a(n) = 6*(3*n-2)! / (n!*(n-1)!*(n+2)!). - Alois P. Heinz, Apr 11 2012
n*(n+2)*a(n) - 3*(3*n-2)*(3*n-4)*a(n-1) = 0. - R. J. Mathar, Aug 10 2015
G.f.: x*3F2(1,2/3,4/3;2,4;27x). - R. J. Mathar, Aug 10 2015
Showing 1-3 of 3 results.