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

%I A092489 #15 Aug 21 2019 10:58:01
%S A092489 0,0,1,4,14,48,165,568,1954,6717,23082,79307,272470,936065,3215741,
%T A092489 11047122,37950140,130369334,447853808,1538496047,5285135093,
%U A092489 18155807539,62369881206,214256590058,736026444181,2528439830821
%N A092489 Arises in enumeration of 321-hexagon-avoiding permutations.
%H A092489 Colin Barker, <a href="/A092489/b092489.txt">Table of n, a(n) for n = 1..1000</a>
%H A092489 Z. Stankova and J. West, <a href="https://doi.org/10.1016/j.disc.2003.06.003">Explicit enumeration of 321, hexagon-avoiding permutations</a>, Discrete Math., 280 (2004), 165-189.
%H A092489 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,9,-4,-4,1).
%F A092489 Stankova and West give an explicit recurrence.
%F A092489 a(n) = A058094(n) - A058094(n-1) for n >= 3. - _Emeric Deutsch_, May 04 2004
%F A092489 From _Colin Barker_, Aug 20 2019: (Start)
%F A092489 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).
%F A092489 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.
%F A092489 (End)
%p A092489 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).
%o A092489 (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
%Y A092489 Cf. A058094, A092490, A092491, A092492.
%K A092489 nonn,easy
%O A092489 1,4
%A A092489 _N. J. A. Sloane_, Apr 04 2004
%E A092489 More terms from _Emeric Deutsch_, May 04 2004