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%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
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