A276837 Number A(n,k) of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most k elements; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 6, 5, 1, 0, 1, 1, 2, 6, 12, 8, 1, 0, 1, 1, 2, 6, 24, 25, 13, 1, 0, 1, 1, 2, 6, 24, 60, 57, 21, 1, 0, 1, 1, 2, 6, 24, 120, 150, 124, 34, 1, 0, 1, 1, 2, 6, 24, 120, 360, 399, 268, 55, 1, 0

Offset

0,13

Comments

The sequence of column k satisfies a linear recurrence with constant coefficients of order 2^(k-1) for k>0.

Links

Alois P. Heinz, Antidiagonals n = 0..30, flattened

Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019

Formula

A(n,k+1) - A(n,k) = A263757(n,k) for n>0.

Example

Square array A(n,k) begins:
  1, 1,  1,   1,    1,    1,    1,     1,     1, ...
  0, 1,  1,   1,    1,    1,    1,     1,     1, ...
  0, 1,  2,   2,    2,    2,    2,     2,     2, ...
  0, 1,  3,   6,    6,    6,    6,     6,     6, ...
  0, 1,  5,  12,   24,   24,   24,    24,    24, ...
  0, 1,  8,  25,   60,  120,  120,   120,   120, ...
  0, 1, 13,  57,  150,  360,  720,   720,   720, ...
  0, 1, 21, 124,  399, 1050, 2520,  5040,  5040, ...
  0, 1, 34, 268, 1145, 3192, 8400, 20160, 40320, ...

Crossrefs

Columns k=0-10 give: A000007, A000012, A000045(n+1), A214663, A276838, A276839, A276840, A276841, A276842, A276843, A276844.

Main diagonal gives A000142.

Cf. A263757, A276719.

Sequence in context: A182172 A143841 A276719 * A269941 A035440 A029878

Adjacent sequences: A276834 A276835 A276836 * A276838 A276839 A276840

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 20 2016

Status

approved