A092492 Arises in enumeration of 321-hexagon-avoiding permutations.

0, 0, 0, 0, 0, 1, 5, 19, 68, 240, 839, 2911, 10054, 34641, 119203, 409893, 1408873, 4841373, 16634350, 57149111, 196333312, 674477710, 2317047808, 7959739375, 27343914410, 93933688630, 322686958885, 1108513737048, 3808031504891

Offset: 1

Author

N. J. A. Sloane, Apr 04 2004

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• 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 (6,-11,9,-4,-4,1).

Crossrefs

Cf. A058094, A092489, A092490, A092491.

Programs

Maple

b[1]:=1: b[2]:=2: b[3]:=5: b[4]:=14: b[5]:=42: b[6]:=132: for n from 6 to 45 do b[n+1]:=6*b[n]-11*b[n-1]+9*b[n-2]-4*b[n-3]-4*b[n-4]+b[n-5] od: a[1]:=0: a[2]:=0: a[3]:=0: a[4]:=0: a[5]:=0: for n from 6 to 40 do a[n]:=2*b[n-3]-5*b[n-4]+b[n-5] od: seq(a[n],n=1..40); # Emeric Deutsch, Jun 08 2004

Mathematica

LinearRecurrence[{6,-11,9,-4,-4,1},{0,0,0,0,0,1,5},30] (* Harvey P. Dale, Jan 31 2025 *)

PARI

concat([0,0,0,0,0], Vec(x^6*(1 - x) / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6) + O(x^30))) \\ Colin Barker, Aug 21 2019

Formula

a(n) = 2*A058094(n-3) - 5*A058094(n-4) + A058094(n-5) for n >= 6. - Emeric Deutsch, Jun 08 2004

From Colin Barker, Aug 21 2019: (Start)

G.f.: x^6*(1 - x) / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6).

a(n) = 6*a(n-1) - 11*a(n-2) + 9*a(n-3) - 4*a(n-4) - 4*a(n-5) + a(n-6) for n>7.

(End)

Extensions

More terms from Emeric Deutsch, Jun 08 2004