A116771 Number of permutations of length n which avoid the patterns 1243, 4132, 4321.

1, 2, 6, 21, 74, 237, 668, 1667, 3750, 7743, 14898, 27033, 46698, 77369, 123672, 191639, 288998, 425499, 613278, 867261, 1205610, 1650213, 2227220, 2967627, 3907910, 5090711, 6565578, 8389761, 10629066, 13358769, 16664592, 20643743, 25406022, 31074995, 37789238

Offset

1,2

Links

Table of n, a(n) for n=1..35.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 114.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: -x*(x^9-3*x^8+3*x^7-4*x^6+19*x^5-32*x^4+27*x^3-18*x^2+6*x-1)/(x-1)^8.

For n >= 3, a(n) = (n^7 + 21*n^6 - 161*n^5 + 525*n^4 - 1316*n^3 + 9534*n^2 - 31284*n + 37800)/2520. - Franklin T. Adams-Watters, Sep 16 2006 [corrected by Jason Yuen, Sep 17 2025]

Mathematica

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 6, 21, 74, 237, 668, 1667, 3750, 7743}, 30] (* Harvey P. Dale, Mar 30 2024 *)

Crossrefs

Sequence in context: A148487 A148488 A148489 * A294765 A116745 A116831

Adjacent sequences: A116768 A116769 A116770 * A116772 A116773 A116774

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from Jason Yuen, Sep 17 2025

Status

approved