cp's OEIS Frontend

A129776 Number of maximally-clustered hexagon-avoiding permutations in S_n; the maximally-clustered hexagon-avoiding permutations are those that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234, 56781234.

%I A129776 #17 Jan 12 2025 17:15:16
%S A129776 1,1,2,6,21,78,298,1157,4535,17872,70644,279704,1108462,4395045,
%T A129776 17431206,69144643,274300461,1088215370,4317321235,17128527716,
%U A129776 67956202025,269612504850,1069675361622,4243893926396,16837490364983,66802139457897,265035151393777
%N A129776 Number of maximally-clustered hexagon-avoiding permutations in S_n; the maximally-clustered hexagon-avoiding permutations are those that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234, 56781234.
%C A129776 If w is maximally-clustered and hexagon-avoiding, there are simple explicit formulas for all the Kazhdan-Lusztig polynomials P_{x,w}.
%D A129776 Jozsef Losonczy, Maximally clustered elements and Schubert varieties,  Ann. Comb. 11 (2007), no. 2, 195-212.
%H A129776 H. Denoncourt and B. Jones, <a href="http://arXiv.org/abs/0704.3469">The enumeration of maximally clustered permutations</a>.
%H A129776 B. Jones, <a href="http://www.arXiv.org/abs/0704.3067">Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations</a>.
%F A129776 G.f.: 1+(3x^6+x^5-5x^4+7x^3-5x^2+x) / (-3x^6+4x^5+8x^4-14x^3+15x^2-7x+1).
%e A129776 a(8)=4535 because there are 4535 permutations of size 8 that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234 and 56781234.
%o A129776 (PARI) lista(nt) = { my(x = 'x + 'x*O('x^nt) ); P = (3*x^6+x^5-5*x^4+7*x^3-5*x^2+x) / (-3*x^6+4*x^5+8*x^4-14*x^3+15*x^2-7*x+1); print(Vec(P));} \\ _Michel Marcus_, Mar 17 2013
%Y A129776 Cf. A058094, A108600.
%K A129776 nonn
%O A129776 0,3
%A A129776 Brant Jones (brant(AT)math.washington.edu), May 17 2007
%E A129776 More terms from _Michel Marcus_, Mar 17 2013
%E A129776 a(0)=1 prepended by _Alois P. Heinz_, Jan 12 2025