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 A058094 Number of 321-hexagon-avoiding permutations in S_n, i.e., permutations of 1..n with no submatrix equivalent to 321, 56781234, 46781235, 56718234 or 46718235. 9
 1, 1, 2, 5, 14, 42, 132, 429, 1426, 4806, 16329, 55740, 190787, 654044, 2244153, 7704047, 26455216, 90860572, 312090478, 1072034764, 3682565575, 12650266243, 43456340025, 149282561256, 512821712570, 1761669869321, 6051779569463, 20789398928496, 71416886375493 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS If y is 321-hexagon avoiding, there are simple explicit formulas for all the Kazhdan-Lusztig polynomials P_{x,y} and the Kazhdan-Lusztig basis element C_y is the product of C_{s_i}'s corresponding to any reduced word for y. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 S. C. Billey and G. S. Warrington, Kazhdan-Lusztig Polynomials for 321-hexagon-avoiding permutations, arXiv:math/0005052 [math.CO], 2000; J. Alg. Combinatorics, Vol. 13, No. 2 (March 2001), 111-136, DOI:10.1023/A:1011279130416. 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 a(n+1) = 6a(n) - 11a(n-1) + 9a(n-2) - 4a(n-3) - 4a(n-4) + a(n-5) for n >= 5. O.g.f.: 1 -x*(1-4*x+4*x^2-3*x^3-x^4+x^5)/(-1+6*x-11*x^2+9*x^3-4*x^4 -4*x^5 +x^6). - R. J. Mathar, Dec 02 2007 EXAMPLE Since the Catalan numbers count 321-avoiding permutations in S_n, a(8) = 1430 - 4 = 1426 subtracting the four forbidden hexagon patterns. MAPLE a[0]:=1: a[1]:=1: a[2]:=2: a[3]:=5: a[4]:=14: a[5]:=42: for n from 5 to 35 do a[n+1]:=6*a[n]-11*a[n-1]+9*a[n-2]-4*a[n-3]-4*a[n-4]+a[n-5] od: seq(a[n], n=0..35); MATHEMATICA LinearRecurrence[{6, -11, 9, -4, -4, 1}, {1, 2, 5, 14, 42, 132}, 40] (* Harvey P. Dale, Nov 09 2012 *) CROSSREFS Cf. A000108, A092489, A092490, A092491, A092492, A092493. Sequence in context: A261589 A036768 A287970 * A080938 A054394 A261590 Adjacent sequences:  A058091 A058092 A058093 * A058095 A058096 A058097 KEYWORD nice,nonn,easy AUTHOR Sara Billey, Dec 03 2000 EXTENSIONS More terms from Emeric Deutsch, May 04 2004 a(0) prepended by Alois P. Heinz, Sep 21 2014 STATUS approved

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Last modified August 18 04:47 EDT 2022. Contains 356204 sequences. (Running on oeis4.)