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A333706
Number T(n,k) of permutations p of [n] such that |p(i+k) - p(i)| <> k for i in [n-k]; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
15
1, 0, 1, 0, 0, 2, 0, 0, 4, 6, 0, 2, 16, 20, 24, 0, 14, 44, 80, 108, 120, 0, 90, 200, 384, 544, 672, 720, 0, 646, 1288, 2240, 3264, 4128, 4800, 5040, 0, 5242, 9512, 15424, 23040, 28992, 34752, 38880, 40320, 0, 47622, 78652, 123456, 176832, 231936, 280512, 323520, 352800, 362880
OFFSET
0,6
COMMENTS
T(n,k) is defined for n,k >= 0. The triangle contains only the terms with k<=n. T(n,k) = n! for k>=n.
LINKS
Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS: Electronic Journal of Combinatorial Number Theory, Vol. 6 (2006), #A11.
Wikipedia, Permutation
EXAMPLE
Triangle T(n,k) begins:
1;
0, 1;
0, 0, 2;
0, 0, 4, 6;
0, 2, 16, 20, 24;
0, 14, 44, 80, 108, 120;
0, 90, 200, 384, 544, 672, 720;
0, 646, 1288, 2240, 3264, 4128, 4800, 5040;
0, 5242, 9512, 15424, 23040, 28992, 34752, 38880, 40320;
...
CROSSREFS
Columns k=0-10 (for n>=k) give: A000007, A002464, A110128, A117574, A189255, A189256, A189271, A360384, A360386, A360462, A360463.
Main diagonal gives A000142.
T(2n,n) gives A189849.
T(n+1,n) gives 4*A138772(n).
T(n+2,n) gives 16*A333804(n).
Cf. A000170 (condition is satisfied for all k), A248686 (p(i) at distance k are sorted).
Sequence in context: A244138 A284611 A282551 * A056676 A352450 A098699
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Apr 02 2020
STATUS
approved