%I #22 Mar 28 2021 04:05:37
%S 1,1,2,6,23,1,103,10,6,1,513,75,74,26,17,9,6,2762,522,645,321,290,130,
%T 166,47,54,48,41,4,8,2,15793,3579,5023,3058,3232,1527,2228,874,1159,
%U 893,875,340,503,281,269,207,156,112,123,21,54,2,0,6,5
%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 1324. 0 <= k <= A342853(n).
%C Equivalently the table for the pattern 4231.
%C First column is A061552.
%H Peter Kagey, <a href="/A342861/b342861.txt">Rows n = 0..13, flattened</a>, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link.
%H FindStat <a href="http://www.findstat.org/StatisticsDatabase/St000405">St000405: The number of occurrences of the pattern 1324 in a permutation</a>.
%H Anders Kaseorg, <a href="https://codegolf.stackexchange.com/a/222494/53884">Answer: Patterns in Permutations</a>, Code Golf Stack Exchange.
%e Triangle 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, 10, 6, 1;
%e 6 | 513, 75, 74, 26, 17, 9, 6;
%e 7 | 2762, 522, 645, 321, 290, 130, 166, ...
%e 8 | 15793, 3579, 5023, 3058, 3232, 1527, 2228, ...
%e 9 | 94776, 24670, 37549, 26174, 30409, 15966, 23762, ...
%e 10 | 591950, 172198, 277089, 213122, 264667, 154452, 228665, ...
%e 11 | 3824112, 1219974, 2043416, 1693787, 2213548, 1420513, 2086877, ...
%Y Cf. A061552, A342853.
%Y Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342862 (2143), A342863 (1243), A342864 (1432), A342865 (1234).
%K nonn,tabf
%O 0,3
%A _Peter Kagey_, Mar 26 2021