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

1,7

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

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)

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

Prog

(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

Crossrefs

Cf. A058094, A092489, A092490, A092491.

Sequence in context: A104496 A001435 A359293 * A070857 A143954 A047145

Adjacent sequences: A092489 A092490 A092491 * A092493 A092494 A092495

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 04 2004

Extensions

More terms from Emeric Deutsch, Jun 08 2004

Status

approved