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A342865
Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 1234. 0 <= k <= A000332(n).
6
1, 1, 2, 6, 23, 1, 103, 12, 4, 0, 0, 1, 513, 102, 63, 10, 6, 12, 8, 0, 0, 5, 0, 0, 0, 0, 0, 1, 2761, 770, 665, 196, 146, 116, 142, 46, 10, 72, 32, 24, 0, 13, 0, 12, 18, 0, 0, 10, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
0,3
COMMENTS
Equivalently the table for the pattern 4321.
First column is A005802.
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.
EXAMPLE
Table begins:
n\k| 0 1 2 3 4 5 6
---+-------------------------------------------------------------------
0 | 1;
1 | 1;
2 | 2;
3 | 6;
4 | 23, 1;
5 | 103, 12, 4, 0, 0, 1;
6 | 513, 102, 63, 10, 6, 12, 8, ...
7 | 2761, 770, 665, 196, 146, 116, 142, ...
8 | 15767, 5545, 5982, 2477, 2148, 1204, 1782, ...
9 | 94359, 39220, 49748, 25886, 25190, 13188, 19936, ...
10 | 586590, 276144, 396642, 244233, 260505, 142550, 210663, ...
11 | 3763290, 1948212, 3089010, 2167834, 2493489, 1476655, 2136586, ...
CROSSREFS
Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342861 (1324), A342862 (2143), A342863 (1243), A342864 (1432).
Sequence in context: A342862 A342863 A342864 * A350274 A350273 A264319
KEYWORD
nonn,tabf
AUTHOR
Peter Kagey, Mar 26 2021
STATUS
approved