OFFSET
0,2
COMMENTS
For n > 0, a(n) is the number of up-down permutations of length 2n + 1 with no four-term increasing subsequence. Equivalently, this is the number of up-down permutations of length 2n + 1 with no four-term decreasing subsequence; the number of down-up permutations of length 2n + 1 with no four-term increasing subsequence; and the number of down-up permutations of length 2n + 1 with no four-term decreasing subsequence. (An up-down permutation is one whose descent set is {2, 4, 6, ...}.). - Joel B. Lewis, Oct 05 2009
REFERENCES
For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..700
Joerg Arndt, The a(3)=168 Young tableaux of shape [4,3,2].
Joel B. Lewis, Pattern avoidance and RSK-like algorithms for alternating permutations and Young tableaux, arXiv:0909.4966 [math.CO], 2009-2011. [Joel B. Lewis, Oct 05 2009]
Joel B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.
Sherry H. F. Yan, On Wilf equivalence for alternating permutations, Elect. J. Combinat.; 20 (2013), #P58.
FORMULA
a(n) = 16*(3*n)!/((n-1)!*(n+1)!*(n+3)!).
(n-1)*(n+3)*(n+1)*a(n) -3*n*(3*n-1)*(3*n-2)*a(n-1)=0, n>1. - R. J. Mathar, Aug 10 2015
G.f.: 2x*3F2(5/3,4/3,2;3,5;27x). - R. J. Mathar, Aug 10 2015
MATHEMATICA
f[n_]:=16 (3 n)!/((n-1)! (n+1)! (n+3)!)
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@ {n + 1, n, n - 1}, {n, 0, 17}] (* Robert G. Wilson v *)
PROG
(PARI) for(n=0, 25, print1(16*(3*n)!/((n-1)!*(n+1)!*(n+3)!), ", ")) \\ G. C. Greubel, Oct 15 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amitai Regev (amitai.regev(AT)weizmann.ac.il), Nov 15 2006
STATUS
approved