

A116731


Number of permutations of length n which avoid the patterns 321, 2143, 3124; or avoid the patterns 132, 2314, 4312, etc.


6



1, 2, 5, 12, 25, 46, 77, 120, 177, 250, 341, 452, 585, 742, 925, 1136, 1377, 1650, 1957, 2300, 2681, 3102, 3565, 4072, 4625, 5226, 5877, 6580, 7337, 8150, 9021, 9952, 10945, 12002, 13125, 14316, 15577, 16910, 18317, 19800, 21361, 23002, 24725, 26532
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Row sums of triangle A130154. Also, binomial transform of [1, 1, 2, 2, 0, 0, 0,...].  Gary W. Adamson, Oct 23 2007
Conjecture: also counts the distinct pairs (flips, iterations) that a bubble sort program generates when sorting all permutations of 1..n.  Wouter Meeussen, Dec 13 2008
A006527+1=A116731.  Vladimir Joseph Stephan Orlovsky, May 04 2011
a(n) is the number of lattice points (x,y) in the closed region bounded by the parabolas y = x(x  n) and y = x(n  x).  Clark Kimberling, Jun 01 2013


LINKS

Table of n, a(n) for n=1..44.
GuoNiu Han, Enumeration of Standard Puzzles
GuoNiu Han, Enumeration of Standard Puzzles [Cached copy]
Sergey Kitaev, Jeffrey Remmel, Mark Tiefenbruck, Quadrant Marked Mesh Patterns in 132Avoiding Permutations II, Electronic Journal of Combinatorial Number Theory, Volume 15 #A16. (arXiv:1302.2274)
Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1)


FORMULA

G.f.: A(x) = {(3x^22x+1)x}/{(x1)^4}
a(n) = (n^33*n^2+5*n)/3.  Franklin T. AdamsWatters, Sep 13 2006


MATHEMATICA

Table[(n^33*n^2+5*n)/3, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)


CROSSREFS

Cf. A006527, A130154.
Sequence in context: A096584 A002836 A116720 * A116722 A116730 A240847
Adjacent sequences: A116728 A116729 A116730 * A116732 A116733 A116734


KEYWORD

nonn,easy


AUTHOR

Lara Pudwell, Feb 26 2006


EXTENSIONS

More terms from Franklin T. AdamsWatters, Sep 13 2006


STATUS

approved



