A116774 Number of permutations of length n which avoid the patterns 2143, 2341, 4312; or avoid the patterns 1234, 1432, 3412.

1, 2, 6, 21, 69, 198, 498, 1121, 2305, 4402, 7910, 13509, 22101, 34854, 53250, 79137, 114785, 162946, 226918, 310613, 418629, 556326, 729906, 946497, 1214241, 1542386, 1941382, 2422981, 3000341, 3688134, 4502658, 5461953, 6585921, 7896450, 9417542, 11175445

Offset

1,2

Links

Table of n, a(n) for n=1..36.

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.: -x*(x^6-5*x^5+13*x^4-14*x^3+13*x^2-5*x+1)/(x-1)^7.

a(n) = (n^6 - 3*n^5 + 10*n^4 - 15*n^3 + 79*n^2 - 72*n + 180)/180. - Franklin T. Adams-Watters, Sep 16 2006

Crossrefs

Sequence in context: A116842 A294708 A294709 * A116756 A116813 A116765

Adjacent sequences: A116771 A116772 A116773 * A116775 A116776 A116777

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from Jason Yuen, Sep 17 2025

Status

approved