A342863 Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 1243. 0 <= k <= A028723(n + 1).

1, 1, 2, 6, 23, 1, 103, 11, 4, 2, 513, 88, 56, 32, 14, 7, 9, 0, 0, 1, 2761, 638, 543, 341, 235, 138, 173, 51, 42, 47, 34, 6, 17, 4, 0, 7, 1, 0, 2, 15767, 4478, 4600, 3119, 2658, 1710, 2180, 972, 975, 877, 771, 356, 542, 233, 184, 266, 157, 81, 130, 41, 60, 49, 16, 16, 37, 8, 9, 13, 3, 0, 10, 1, 0, 0, 0, 0, 1

Offset: 0

Author

Peter Kagey, Mar 26 2021

Keywords

• nonn
• tabf

Comments

Equivalently the table for the patterns 2134, 3421, and 4312.

First column is A005802.

Examples

			Table 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,      56,      32,      14,       7,       9, ...
   7 |    2761,     638,     543,     341,     235,     138,     173, ...
   8 |   15767,    4478,    4600,    3119,    2658,    1710,    2180, ...
   9 |   94359,   31199,   36691,   26602,   25756,   17628,   22984, ...
  10 |  586590,  218033,  284370,  218957,  231390,  166338,  221429, ...
  11 | 3763290, 1535207, 2174352, 1767837, 1994176, 1496134, 2028316, ...
		

Links

• Peter Kagey, Rows n = 0..13, flattened, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link.
• 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), A342862 (2143), A342864 (1432), A342865 (1234).