A231166 Number of permutations of [n] avoiding simultaneously consecutive patterns 1243, 1342, and 1324.

1, 1, 2, 6, 21, 91, 467, 2755, 18523, 139740, 1169616, 10763807, 108028386, 1174391384, 13748315494, 172439034531, 2306986699190, 32792999417180, 493559520202535, 7841127918788283, 131127477517244419, 2302491655047553206, 42355105188617740229

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..70

A. Baxter, B. Nakamura, and D. Zeilberger, Automatic generation of theorems and proofs on enumerating consecutive Wilf-classes, 2011.

S. Kitaev and T. Mansour, On multi-avoidance of generalized patterns, arXiv:math/0209340 [math.CO], 2002.

Example

a(4) = 24 - 3 = 21 because 1243, 1342, 1324 are avoided.

Maple

b:= proc(u, o, s, t) option remember; `if`(u+o=0, 1,
       add(b(u-j, o+j-1, `if`(t>0, t, 0), `if`(t>0, -j, 0)),
           j=`if`(s>0 and t>0, s+t-1, 1)..u)+
       add(b(u+j-1, o-j, `if`(t>0, t, 0), +j),
           j=1..`if`(s>0 and t<0 and -t<s, -t-1, o)))
    end:
a:= n-> b(n, 0$3):
seq(a(n), n=0..25);

Mathematica

b[u_, o_, s_, t_] := b[u, o, s, t] = If[u + o == 0, 1, Sum[b[u - j, o + j - 1, If[t > 0, t, 0], If[t > 0, -j, 0]], {j, If[s > 0 && t > 0, s + t - 1, 1], u}] + Sum[b[u + j - 1, o - j, If[t > 0, t, 0], +j], {j, 1, If[s > 0 && t < 0 && -t < s, -t - 1, o]}]];
a[n_] := b[n, 0, 0, 0];
a /@ Range[0, 25] (* Jean-François Alcover, Feb 27 2020, after Alois P. Heinz *)

Crossrefs

Cf. A113228, A117156, A117226.

Sequence in context: A177479 A367100 A147719 * A115089 A304196 A266328

Adjacent sequences: A231163 A231164 A231165 * A231167 A231168 A231169

Keyword

nonn

Author

Alois P. Heinz, Nov 04 2013

Status

approved