A249631 Number of permutations p of {1,...,n} such that |p(i+1)-p(i)| < k, k=2,...,n; T(n,k), read by rows.

2, 2, 6, 2, 12, 24, 2, 20, 72, 120, 2, 34, 180, 480, 720, 2, 56, 428, 1632, 3600, 5040, 2, 88, 1042, 5124, 15600, 30240, 40320, 2, 136, 2512, 15860, 61872, 159840, 282240, 362880, 2, 208, 5912, 50186, 236388, 773040, 1764000, 2903040, 3628800

Offset

2,1

Links

Table of n, a(n) for n=2..46.

Li-yao Xia, Triangle of T(n,k) for n=2..10, k=2..n

Example

Triangle starts with n=2:
2;
2,  6;
2, 12,  24;
2, 20,  72, 120;
2, 34, 180, 480, 720;

Prog

(Haskell) a n x = filter (\l -> all (< x) (zipWith (\x y -> abs (x - y)) l (tail l))) (permutations [1 .. n])
(PARI) isokp(perm, k) = {for (i=1, #perm-1, if (abs(perm[i]-perm[i+1]) >= k, return (0)); ); return (1); }
tabl(nn) = {for (n=2, nn, for (k=2, n, print1(sum(i=1, n!, isokp(numtoperm(n, i), k)), ", "); ); print(); ); } \\ Michel Marcus, Nov 06 2014

Crossrefs

Cf. A000142, main diagonal, A062119, subdiagonal.

Cf. A003274, A174700, A174701, A174702, 2nd to 5th columns, T(n,k), k=3,4,5,6.

Cf. A174703, A174704, A174705, A174706, A174707, A174708, similar definitions.

Sequence in context: A284012 A278243 A071223 * A055934 A096217 A281145

Adjacent sequences: A249628 A249629 A249630 * A249632 A249633 A249634

Keyword

nonn,tabl

Author

Li-yao Xia, Nov 02 2014

Status

approved