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A231166
Number of permutations of [n] avoiding simultaneously consecutive patterns 1243, 1342, and 1324.
4
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 04 2013
STATUS
approved