A342864 Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 1432. 0 <= k <= A100354(n).

1, 1, 2, 6, 23, 1, 103, 11, 5, 0, 1, 513, 87, 68, 17, 18, 10, 0, 4, 2, 0, 1, 2761, 625, 626, 268, 274, 138, 112, 58, 51, 44, 31, 9, 15, 8, 12, 0, 5, 0, 0, 0, 3, 15767, 4378, 5038, 2781, 3060, 1697, 1817, 1036, 964, 773, 656, 450, 379, 320, 285, 148, 237, 97, 98, 55, 68, 61, 23, 30, 30, 13, 30, 0, 0, 0, 16, 0, 10, 0, 0, 1, 0, 0, 0, 0, 2

Offset: 0

Author

Peter Kagey, Mar 26 2021

Keywords

• nonn
• tabf

Comments

Equivalently the table for the patterns 2341, 3214, and 4123.

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,       5,       0,       1;
   6 |     513,      87,      68,      17,      18,      10,       0, ...
   7 |    2761,     625,     626,     268,     274,     138,     112, ...
   8 |   15767,    4378,    5038,    2781,    3060,    1697,    1817, ...
   9 |   94359,   30671,   38541,   24731,   28881,   17943,   21193, ...
  10 |  586590,  216883,  289785,  205853,  251051,  170941,  211942, ...
  11 | 3763290, 1552588, 2172387, 1663964, 2096207, 1535129, 1954751, ...
		

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, A100354.

Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342861 (1324), A342862 (2143), A342863 (1243), A342865 (1234).