A342863 - OEIS

%I #19 Mar 28 2021 04:05:52

%S 1,1,2,6,23,1,103,11,4,2,513,88,56,32,14,7,9,0,0,1,2761,638,543,341,

%T 235,138,173,51,42,47,34,6,17,4,0,7,1,0,2,15767,4478,4600,3119,2658,

%U 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

%N 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).

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

%C First column is A005802.

%H Peter Kagey, <a href="/A342863/b342863.txt">Rows n = 0..13, flattened</a>, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link.

%H Anders Kaseorg, <a href="https://codegolf.stackexchange.com/a/222494/53884">Answer: Patterns in Permutations</a>, Code Golf Stack Exchange.

%e Table begins:

%e   n\k|       0        1        2        3        4        5        6

%e   ---+-------------------------------------------------------------------

%e    0 |       1;

%e    1 |       1;

%e    2 |       2;

%e    3 |       6;

%e    4 |      23,       1;

%e    5 |     103,      11,       4,       2;

%e    6 |     513,      88,      56,      32,      14,       7,       9, ...

%e    7 |    2761,     638,     543,     341,     235,     138,     173, ...

%e    8 |   15767,    4478,    4600,    3119,    2658,    1710,    2180, ...

%e    9 |   94359,   31199,   36691,   26602,   25756,   17628,   22984, ...

%e   10 |  586590,  218033,  284370,  218957,  231390,  166338,  221429, ...

%e   11 | 3763290, 1535207, 2174352, 1767837, 1994176, 1496134, 2028316, ...

%Y Cf. A005802, A028723.

%Y Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342861 (1324), A342862 (2143), A342864 (1432), A342865 (1234).

%K nonn,tabf

%O 0,3

%A _Peter Kagey_, Mar 26 2021