A346462 - OEIS

A346462

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.

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

0,6

COMMENTS

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.

Column k=0 is A002464. Columns k=2 and k=3 are given by A086852.

Main diagonal begins: 1,0,2,2,8,14,54,128,498,1426,5736,... A363181.

LINKS

Alois P. Heinz, Rows n = 0..20, flattened

FindStat, St000064: The number of one-box pattern of a permutation.

S. Kitaev, J. Remmel, The 1-box pattern on pattern avoiding permutations, arXiv:1305.6970 [math.CO], 2013.

EXAMPLE

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

CROSSREFS

Cf. A002464, A086852, A229729, A229730, A363181.

Row sums give A000142.

Sequence in context: A350785 A158118 A212137 * A230295 A147592 A108885

Adjacent sequences: A346459 A346460 A346461 * A346463 A346464 A346465

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Jul 19 2021

STATUS

approved