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

1,4

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).

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)

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).

Prog

(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

Crossrefs

Cf. A058094, A092490, A092491, A092492.

Sequence in context: A289928 A204089 A007070 * A094827 A094667 A370051

Adjacent sequences: A092486 A092487 A092488 * A092490 A092491 A092492

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 04 2004

Extensions

More terms from Emeric Deutsch, May 04 2004

Status

approved