A263788 Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of permutations of n and convexity k.

1, 1, 2, 4, 0, 0, 2, 6, 2, 0, 8, 4, 4, 8, 6, 2, 28, 20, 32, 12, 12, 8, 16, 6, 106, 80, 156, 120, 132, 48, 48, 8, 32, 16, 352, 396, 708, 696, 1044, 624, 684, 240, 240, 8, 58, 36, 1174, 1654, 3698, 3716, 6396, 5832, 6756, 3936, 4176, 1440, 1440, 8, 98, 80, 3752

Offset

0,3

Comments

The convexity of a permutation in one-line notation is the maximal value of twice an entry minus the sum of its neighbors.

The row lengths are 2n-2 starting for n>=3.

Row sums give A000142.

Links

Table of n, a(n) for n=0..60.

FindStat - Combinatorial Statistic Finder, The convexity of a permutation.

Example

Triangle begins:
  1
  1
  2
  4  0 0   2
  6  2 0   8  4   4
  8  6 2  28 20  32  12  12
  8 16 6 106 80 156 120 132 48 48
  ...

Crossrefs

Cf. A000142.

Sequence in context: A028586 A253179 A300723 * A355335 A292144 A300324

Adjacent sequences: A263785 A263786 A263787 * A263789 A263790 A263791

Keyword

nonn,tabf

Author

Christian Stump, Oct 26 2015

Extensions

More terms from Alois P. Heinz, Oct 26 2015

Status

approved