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A346462
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Triangle read by rows: T(n,k) gives the number of permutations of length n containing exactly k instances of the 1-box pattern; 0 <= k <= n.
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2
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1, 1, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 10, 4, 8, 14, 0, 40, 10, 42, 14, 90, 0, 230, 40, 226, 80, 54, 646, 0, 1580, 230, 1480, 442, 534, 128, 5242, 0, 12434, 1580, 11496, 2920, 4746, 1404, 498, 47622, 0, 110320, 12434, 101966, 22762, 45216, 13138, 7996, 1426
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OFFSET
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0,6
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COMMENTS
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An instance of the 1-box pattern in a permutation pi is a letter pi_i such that pi_{i-1} or pi_{i+1} differs from pi_i by exactly 1.
Main diagonal begins: 1,0,2,2,8,14,54,128,498,1426,5736,... A363181.
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LINKS
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EXAMPLE
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The permutation 14327568 has 5 instances of the 1-box pattern:
- position 2 differs from position 3 by one,
- position 3 differs from positions 2 and 4 by one,
- position 4 differs from position 3 by one,
- position 6 differs from position 7 by one,
- position 7 differs from position 6 by one, and
positions 1, 5, and 8 differ from all of their neighbors by more than 1.
Table begins:
n\k| 0 1 2 3 4 5 6
-----+-----------------------------
0 | 1
1 | 1 0
2 | 0 0 2
3 | 0 0 4 2
4 | 2 0 10 4 8
5 | 14 0 40 10 42 14
6 | 90 0 230 40 226 80 54
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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