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A342840
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Irregular triangle: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 4213. 0 <= k <= A342646(n).
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7
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1, 1, 2, 6, 23, 1, 103, 10, 6, 1, 512, 77, 69, 30, 21, 5, 6, 2740, 548, 598, 330, 335, 123, 174, 58, 58, 37, 26, 3, 9, 1, 15485, 3799, 4686, 2970, 3411, 1676, 2338, 1040, 1317, 878, 777, 363, 608, 230, 252, 165, 133, 30, 93, 26, 31, 4, 1, 3, 4, 91245, 26165, 35148, 24550, 30182, 17185, 24685, 12976, 16867, 12248, 12360, 7203, 11086, 5692, 6391, 5194, 5006, 2751, 3917, 2019, 2482, 1622, 1371, 812, 1233, 490, 495, 416, 360, 157, 282, 54, 78, 41, 29, 22, 49, 7, 4, 0, 6
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OFFSET
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0,3
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COMMENTS
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The sequence is the same for the patterns 1342, 2431, and 3124.
The sequence appears to be the same for the patterns 1423, 2314, 3241, and 4132.
First column is given by A022558. Row sums given by n!.
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LINKS
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EXAMPLE
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Triangle begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13
----+-------------------------------------------------------------
0 | 1;
1 | 1;
2 | 2;
3 | 6;
4 | 23, 1;
5 | 103, 10, 6, 1;
6 | 512, 77, 69, 30, 21, 5, 6;
7 | 2740, 548, 598, 330, 335, 123, 174, 58, 58, 37, 26, 3, 9, 1;
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MATHEMATICA
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Join@@Array[Table[Length@Select[Permutations@Range@#, Length@Select[Subsets[#, {4}], Ordering@Ordering@#=={4, 2, 1, 3}&]==k&], {k, 0, Binomial[n+1, 4]}]//.{a__, 0}:>{a}&, 8, 0] (* Giorgos Kalogeropoulos, Mar 25 2021 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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