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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 04 2004
EXTENSIONS
More terms from Emeric Deutsch, May 04 2004
STATUS
approved