The On-Line Encyclopedia of Integer Sequences (OEIS)

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A092492

Arises in enumeration of 321-hexagon-avoiding permutations.
(history; published version)

#14 by Alois P. Heinz at Wed Aug 21 05:46:43 EDT 2019

STATUS

reviewed

approved

#13 by Michel Marcus at Wed Aug 21 05:44:28 EDT 2019

STATUS

proposed

reviewed

#12 by Colin Barker at Wed Aug 21 05:43:05 EDT 2019

STATUS

editing

proposed

#11 by Colin Barker at Wed Aug 21 05:42:33 EDT 2019

FORMULA

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)

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

#10 by Colin Barker at Wed Aug 21 05:40:53 EDT 2019

LINKS

Colin Barker, <a href="/A092492/b092492.txt">Table of n, a(n) for n = 1..1000</a>

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,9,-4,-4,1).

STATUS

approved

editing

#9 by Joerg Arndt at Tue Aug 15 03:11:15 EDT 2017

STATUS

proposed

approved

#8 by Michel Marcus at Tue Aug 15 02:19:14 EDT 2017

STATUS

editing

proposed

#7 by Michel Marcus at Tue Aug 15 02:19:08 EDT 2017

REFERENCES

Z. Stankova and J. West, Explicit enumeration of 321, hexagon-avoiding permutations, Discrete Math., 280 (2004), 165-189.

LINKS

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.

CROSSREFS

Cf. A058094, A092489-, A092490, A092491.

STATUS

proposed

editing

#6 by Jon E. Schoenfield at Tue Aug 15 01:16:10 EDT 2017

STATUS

editing

proposed

#5 by Jon E. Schoenfield at Tue Aug 15 01:16:06 EDT 2017

FORMULA

a(n): = 2*A058094(n-3) - 5*A058094(n-4) + A058094(n-5) for n >= 6. - Emeric Deutsch, Jun 08 2004

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

STATUS

approved

editing