A250118 Triangle read by rows: T(n,m) (n >= 1, 1 <= m <= n) = number of set partitions of [n], avoiding 12343, with m blocks.

1, 1, 1, 1, 3, 1, 1, 7, 6, 1, 1, 15, 25, 9, 1, 1, 31, 90, 52, 12, 1, 1, 63, 301, 246, 88, 15, 1, 1, 127, 966, 1039, 510, 133, 18, 1, 1, 255, 3025, 4083, 2569, 909, 187, 21, 1, 1, 511, 9330, 15274, 11790, 5296, 1470, 250, 24, 1, 1, 1023, 28501, 55152, 50644, 27678, 9706, 2220, 322, 27, 1

Offset

1,5

Links

Lars Blomberg, Table of n, a(n) for n = 1..5050 (The first 100 rows.)

Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.

Example

Triangle begins:
  1;
  1,    1;
  1,    3,     1;
  1,    7,     6,     1;
  1,   15,    25,     9,     1;
  1,   31,    90,    52,    12,     1;
  1,   63,   301,   246,    88,    15,    1;
  1,  127,   966,  1039,   510,   133,   18,    1;
  1,  255,  3025,  4083,  2569,   909,  187,   21,   1;
  1,  511,  9330, 15274, 11790,  5296, 1470,  250,  24,  1;
  1, 1023, 28501, 55152, 50644, 27678, 9706, 2220, 322, 27, 1;
  ...

Crossrefs

Cf. A112857, A250119. For diagonals see A000392, A163941.

Sequence in context: A348863 A202181 A130749 * A250119 A154959 A080417

Adjacent sequences: A250115 A250116 A250117 * A250119 A250120 A250121

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 25 2014

Extensions

a(46)-a(66) from Lars Blomberg, Aug 17 2017

Status

approved