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A342861 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).

%I A342861 #22 Mar 28 2021 04:05:37
%S A342861 1,1,2,6,23,1,103,10,6,1,513,75,74,26,17,9,6,2762,522,645,321,290,130,
%T A342861 166,47,54,48,41,4,8,2,15793,3579,5023,3058,3232,1527,2228,874,1159,
%U A342861 893,875,340,503,281,269,207,156,112,123,21,54,2,0,6,5
%N A342861 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 A342861 Equivalently the table for the pattern 4231.
%C A342861 First column is A061552.
%H A342861 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 A342861 FindStat <a href="http://www.findstat.org/StatisticsDatabase/St000405">St000405: The number of occurrences of the pattern 1324 in a permutation</a>.
%H A342861 Anders Kaseorg, <a href="https://codegolf.stackexchange.com/a/222494/53884">Answer: Patterns in Permutations</a>, Code Golf Stack Exchange.
%e A342861 Triangle begins:
%e A342861   n\k|       0        1        2        3        4        5        6
%e A342861   ---+-------------------------------------------------------------------
%e A342861    0 |       1;
%e A342861    1 |       1;
%e A342861    2 |       2;
%e A342861    3 |       6;
%e A342861    4 |      23,       1;
%e A342861    5 |     103,      10,       6,       1;
%e A342861    6 |     513,      75,      74,      26,      17,       9,       6;
%e A342861    7 |    2762,     522,     645,     321,     290,     130,     166, ...
%e A342861    8 |   15793,    3579,    5023,    3058,    3232,    1527,    2228, ...
%e A342861    9 |   94776,   24670,   37549,   26174,   30409,   15966,   23762, ...
%e A342861   10 |  591950,  172198,  277089,  213122,  264667,  154452,  228665, ...
%e A342861   11 | 3824112, 1219974, 2043416, 1693787, 2213548, 1420513, 2086877, ...
%Y A342861 Cf. A061552, A342853.
%Y A342861 Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342862 (2143), A342863 (1243), A342864 (1432), A342865 (1234).
%K A342861 nonn,tabf
%O A342861 0,3
%A A342861 _Peter Kagey_, Mar 26 2021