A356728 The number of 3-permutations that avoid the patterns 132 and 213.

1, 4, 12, 28, 58, 114, 220, 424, 822, 1606, 3160, 6252, 12418, 24730, 49332, 98512, 196846, 393486, 786736, 1573204, 3146106, 6291874, 12583372, 25166328, 50332198, 100663894, 201327240, 402653884, 805307122, 1610613546, 3221226340

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Nathan Sun, On d-permutations and Pattern Avoidance Classes, arXiv:2208.08506 [math.CO], 2022.

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

a(n) = A308580(n-1) - 2.

a(n) = a(n-1) + 3*2^(n-2) + 2*(n-2).

From Stefano Spezia, Aug 27 2022: (Start)

G.f.: x*(1 - x + x^2 - 3*x^3)/((1 - x)^3*(1 - 2*x)).

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 4.

a(n) = 3*2^(n-1) + n^2 - 3*n. (End)

Mathematica

LinearRecurrence[{5, -9, 7, -2}, {1, 4, 12, 28}, {1, 35}] (* Hugo Pfoertner, Aug 27 2022 *)

Crossrefs

Cf. A308580.

Sequence in context: A011939 A203286 A028346 * A079089 A182705 A186924

Adjacent sequences: A356725 A356726 A356727 * A356729 A356730 A356731

Keyword

nonn,easy

Author

Nathan Sun, Aug 24 2022

Status

approved