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0, 0, 0, 0, 1, 6, 25, 93, 333, 1172, 4083, 14137, 48778, 167981, 577874, 1986747, 6828120, 23462470, 80611581, 276944893, 951422603, 3268470411, 11228209786, 38572124196, 132505812826, 455192771711, 1563706508759, 5371738013650
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OFFSET
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1,6
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COMMENTS
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A recurrence relation follows in a straightforward manner from the above formula and the recurrence relation for A058094.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..200
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).
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FORMULA
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From Colin Barker, Aug 21 2019: (Start)
G.f.: x^5 / (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>6.
(End)
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MAPLE
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b[1]:=1:b[2]:=2:b[3]:=5:b[4]:=14:b[5]:=42:b[6]:=132: for n from 6 to 34 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: for n from 5 to 34 do a[n]:=2*b[n-2]-5*b[n-3]+b[n-4]+a[n-1] od: seq(a[n], n=1..34); # Emeric Deutsch, Apr 12 2005
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MATHEMATICA
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LinearRecurrence[{6, -11, 9, -4, -4, 1}, {0, 0, 0, 0, 1, 6}, 40] (* Vincenzo Librandi, Aug 15 2017 *)
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PROG
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(PARI) concat([0, 0, 0, 0], Vec(x^5 / (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
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CROSSREFS
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Cf. A058094, A092489, A092490, A092492.
Sequence in context: A277973 A143815 A209241 * A112308 A034336 A291230
Adjacent sequences: A092488 A092489 A092490 * A092492 A092493 A092494
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Apr 04 2004
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EXTENSIONS
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Edited by Emeric Deutsch, Apr 12 2005
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STATUS
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approved
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