A092493 a(n) = 4a(n-1) - 4a(n-2) + 3a(n-3) + a(n-4) - a(n-5).

1, 2, 5, 14, 42, 128, 389, 1179, 3572, 10825, 32810, 99446, 301412, 913547, 2768863, 8392136, 25435699, 77092976, 233660832, 708201794, 2146486339, 6505777953, 19718339694, 59764246943, 181139247400, 549014312524, 1664005563066

Offset

1,2

Comments

Arises in enumeration of certain pattern-avoiding permutations.

Links

Table of n, a(n) for n=1..27.

Z. Stankova and J. West, Explicit enumeration of 321, hexagon-avoiding permutations, Discrete Math., 280 (2004), 165-189.

Index entries for linear recurrences with constant coefficients, signature (4,-4,3,1,-1).

Formula

G.f.: x*(1 - 2*x + x^2 - x^3 - x^4)/(1 - 4*x + 4*x^2 - 3*x^3 - x^4 + x^5). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009; corrected by R. J. Mathar, Sep 16 2009]

Maple

a[1]:=1: a[2]:=2: a[3]:=5: a[4]:=14: a[5]:=42: for n from 6 to 32 do a[n]:=4*a[n-1]-4*a[n-2]+3*a[n-3]+a[n-4]-a[n-5] od: seq(a[j], j=1..32); # Emeric Deutsch, Apr 12 2005

Mathematica

LinearRecurrence[{4, -4, 3, 1, -1}, {1, 2, 5, 14, 42}, 40] (* Harvey P. Dale, Jul 14 2024 *)

Crossrefs

Cf. A058094, A092489-A092492.

Sequence in context: A293347 A148326 A148327 * A316779 A344571 A148328

Adjacent sequences: A092490 A092491 A092492 * A092494 A092495 A092496

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 04 2004

Extensions

Edited by Emeric Deutsch, Apr 12 2005

Status

approved