A092489 Arises in enumeration of 321-hexagon-avoiding permutations.

0, 0, 1, 4, 14, 48, 165, 568, 1954, 6717, 23082, 79307, 272470, 936065, 3215741, 11047122, 37950140, 130369334, 447853808, 1538496047, 5285135093, 18155807539, 62369881206, 214256590058, 736026444181, 2528439830821

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, A092490, A092491, A092492.

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 35 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: seq(b[n],n=1..35): a[1]:=0: a[2]:=0: for n from 3 to 35 do a[n]:=b[n]-2*b[n-1] od: seq(a[n],n=1..35); # here b[n]=A058094(n).

PARI

concat([0,0], Vec(x^3*(1 - 2*x + x^2 - x^3 - x^4) / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6) + O(x^30))) \\ Colin Barker, Aug 20 2019

Formula

Stankova and West give an explicit recurrence.

a(n) = A058094(n) - A058094(n-1) for n >= 3. - Emeric Deutsch, May 04 2004

From Colin Barker, Aug 20 2019: (Start)

G.f.: x^3*(1 - 2*x + x^2 - x^3 - x^4) / (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, May 04 2004