A116767 Number of permutations of length n which avoid the patterns 1234, 3142, 3421.

1, 2, 6, 21, 71, 208, 526, 1174, 2370, 4416, 7714, 12783, 20277, 31004, 45946, 66280, 93400, 128940, 174798, 233161, 306531, 397752, 510038, 647002, 812686, 1011592, 1248714, 1529571, 1860241, 2247396

Offset

1,2

Links

Table of n, a(n) for n=1..30.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 21.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

G.f.: A(x) = -{x(2x^8-3x^7+x^6-9x^5+15x^4-14x^3+13x^2-5x+1)}/{(x-1)^7}

For n >= 3, a(n) = (n^6 + 45n^5 - 245n^4 - 465n^3 + 8164n^2 - 24780n + 25920)/720. - Franklin T. Adams-Watters, Sep 16 2006

a(1)=1, a(2)=2, a(3)=6, a(4)=21, a(5)=71, a(6)=208, a(7)=526, a(8)=1174, a(9)=2370, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+a (n-7) [From Harvey P. Dale, Aug 31 2011]

Mathematica

Join[{1, 2, 6}, Table[(n^6+45n^5-245n^4-465n^3+8164n^2-24780n+25920)/ 720, {n, 4, 40}]] (* or *) Join[{1, 2}, LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {6, 21, 71, 208, 526, 1174, 2370}, 40]] (* Harvey P. Dale, Aug 31 2011 *)

Crossrefs

Sequence in context: A116795 A116766 A116825 * A116759 A116835 A294725

Adjacent sequences: A116764 A116765 A116766 * A116768 A116769 A116770

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved