A342862 Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 2143. 0 <= k <= A028723(n + 1).

1, 1, 2, 6, 23, 1, 103, 11, 4, 2, 513, 88, 53, 33, 18, 8, 6, 0, 0, 1, 2761, 642, 495, 340, 262, 160, 172, 65, 58, 39, 14, 6, 18, 0, 0, 6, 0, 0, 2, 15767, 4567, 4099, 3007, 2692, 1832, 2171, 1152, 1291, 968, 728, 457, 566, 174, 176, 221, 129, 14, 122, 29, 38, 52, 8, 0, 32, 9, 0, 10, 0, 0, 8, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Peter Kagey, Mar 26 2021

Keywords

• nonn
• tabf

Comments

Equivalently the table for the pattern 3412.

First column is A005802.

Examples

			Triangle begins:
  n\k|       0        1        2        3        4        5        6
  ---+-------------------------------------------------------------------
   0 |       1;
   1 |       1;
   2 |       2;
   3 |       6;
   4 |      23,       1;
   5 |     103,      11,       4,       2;
   6 |     513,      88,      53,      33,      18,       8,       6, ...
   7 |    2761,     642,     495,     340,     262,     160,     172, ...
   8 |   15767,    4567,    4099,    3007,    2692,    1832,    2171, ...
   9 |   94359,   32443,   32345,   25049,   24492,   17732,   21841, ...
  10 |  586590,  232189,  250371,  203452,  211291,  160561,  201524, ...
  11 | 3763290, 1679295, 1926145, 1635315, 1776655, 1409304, 1787218, ...
		

Links

• Peter Kagey, Rows n = 0..13, flattened, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link.
• FindStat, St000407: The number of occurrences of the pattern 2143 in a permutation.
• Anders Kaseorg, Answer: Patterns in Permutations, Code Golf Stack Exchange.

Crossrefs

Cf. A005802, A028723.

Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342861 (1324), A342863 (1243), A342864 (1432), A342865 (1234).