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A092492 Arises in enumeration of 321-hexagon-avoiding permutations.

%I A092492 #16 Jan 31 2025 15:31:09
%S A092492 0,0,0,0,0,1,5,19,68,240,839,2911,10054,34641,119203,409893,1408873,
%T A092492 4841373,16634350,57149111,196333312,674477710,2317047808,7959739375,
%U A092492 27343914410,93933688630,322686958885,1108513737048,3808031504891
%N A092492 Arises in enumeration of 321-hexagon-avoiding permutations.
%H A092492 Colin Barker, <a href="/A092492/b092492.txt">Table of n, a(n) for n = 1..1000</a>
%H A092492 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 A092492 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,9,-4,-4,1).
%F A092492 a(n) = 2*A058094(n-3) - 5*A058094(n-4) + A058094(n-5) for n >= 6. - _Emeric Deutsch_, Jun 08 2004
%F A092492 From _Colin Barker_, Aug 21 2019: (Start)
%F A092492 G.f.: x^6*(1 - x) / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6).
%F A092492 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 A092492 (End)
%p A092492 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
%t A092492 LinearRecurrence[{6,-11,9,-4,-4,1},{0,0,0,0,0,1,5},30] (* _Harvey P. Dale_, Jan 31 2025 *)
%o A092492 (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
%Y A092492 Cf. A058094, A092489, A092490, A092491.
%K A092492 nonn,easy
%O A092492 1,7
%A A092492 _N. J. A. Sloane_, Apr 04 2004
%E A092492 More terms from _Emeric Deutsch_, Jun 08 2004