A346462 - OEIS

%I #25 May 20 2023 05:25:22

%S 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,

%T 54,646,0,1580,230,1480,442,534,128,5242,0,12434,1580,11496,2920,4746,

%U 1404,498,47622,0,110320,12434,101966,22762,45216,13138,7996,1426

%N 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.

%C 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.

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

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

%H Alois P. Heinz, <a href="/A346462/b346462.txt">Rows n = 0..20, flattened</a>

%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000064">St000064: The number of one-box pattern of a permutation</a>.

%H S. Kitaev, J. Remmel, <a href="http://www.arxiv.org/abs/1305.6970">The 1-box pattern on pattern avoiding permutations</a>, arXiv:1305.6970 [math.CO], 2013.

%e The permutation 14327568 has 5 instances of the 1-box pattern:

%e - position 2 differs from position 3 by one,

%e - position 3 differs from positions 2 and 4 by one,

%e - position 4 differs from position 3 by one,

%e - position 6 differs from position 7 by one,

%e - position 7 differs from position 6 by one, and

%e positions 1, 5, and 8 differ from all of their neighbors by more than 1.

%e Table begins:

%e   n\k|  0  1    2   3    4   5   6

%e -----+-----------------------------

%e    0 |  1

%e    1 |  1  0

%e    2 |  0  0    2

%e    3 |  0  0    4   2

%e    4 |  2  0   10   4    8

%e    5 | 14  0   40  10   42  14

%e    6 | 90  0  230  40  226  80  54

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

%Y Row sums give A000142.

%K nonn,tabl

%O 0,6

%A _Peter Kagey_, Jul 19 2021