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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 23 15:00 EST 2020. Contains 332166 sequences. (Running on oeis4.)