A264896 Number of permutations of [n] with exactly one occurrence of the consecutive pattern 45321.

1, 12, 126, 1344, 15110, 180736, 2308548, 31481472, 457520055, 7068885600, 115808906178, 2006533573632, 36674815572540, 705453732298240, 14248697953325160, 301564509817810944, 6674811622886359005, 154228999030804811520, 3713903962096887036390

Offset

5,2

Comments

Consecutive patterns 12354, 21345, 54312 give the same sequence.

Links

Alois P. Heinz, Table of n, a(n) for n = 5..200

Example

a(5) = 1: 45321.
a(6) = 12: 156432, 256431, 356421, 453216, 456321, 463215, 546321, 563214, 564213, 564312, 564321, 645321.

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(
       b(u+j-1, o-j, `if`(u+j-3<j, 0, j)), j=1..o)+convert(series(
      `if`(t=-2, x, 1)*add(b(u-j, o+j-1, `if`(j<t or t=-2, 0,
      `if`(t>0, -1, `if`(t=-1, -2, 0)))), j=1..u), x, 2), polynom))
    end:
a:= n-> coeff(b(n, 0$2), x, 1):
seq(a(n), n=5..25);

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[b[u + j - 1, o - j, If[u + j - 3 < j, 0, j]], {j, 1, o}] + Expand[If[t == -2, x, 1]*Sum[b[u - j, o + j - 1, If[j < t || t == -2, 0, If[t > 0, -1, If[t == -1, -2, 0]]]], {j, 1, u}]]];
a[n_] := Coefficient[b[n, 0, 0], x, 1];
Table[a[n], {n, 5, 25}] (* Jean-François Alcover, Nov 01 2021, after Alois P. Heinz *)

Crossrefs

Column k=1 of A264781.

Sequence in context: A004991 A228008 A101602 * A062199 A199528 A124797

Adjacent sequences: A264893 A264894 A264895 * A264897 A264898 A264899

Keyword

nonn

Author

Alois P. Heinz, Nov 27 2015

Status

approved