A342864 - OEIS

%I #26 Mar 28 2021 07:05:34

%S 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,

%T 268,274,138,112,58,51,44,31,9,15,8,12,0,5,0,0,0,3,15767,4378,5038,

%U 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

%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 1432. 0 <= k <= A100354(n).

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

%C First column is A005802.

%H Peter Kagey, <a href="/A342864/b342864.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,       5,       0,       1;

%e    6 |     513,      87,      68,      17,      18,      10,       0, ...

%e    7 |    2761,     625,     626,     268,     274,     138,     112, ...

%e    8 |   15767,    4378,    5038,    2781,    3060,    1697,    1817, ...

%e    9 |   94359,   30671,   38541,   24731,   28881,   17943,   21193, ...

%e   10 |  586590,  216883,  289785,  205853,  251051,  170941,  211942, ...

%e   11 | 3763290, 1552588, 2172387, 1663964, 2096207, 1535129, 1954751, ...

%Y Cf. A005802, A100354.

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

%K nonn,tabf

%O 0,3

%A _Peter Kagey_, Mar 26 2021