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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
OFFSET
2,1
COMMENTS
T(21,18) > 2^64. - Tamás Fülöp, Dec 13 2025
LINKS
Tamás Fülöp, Rows n=2..20 of triangle, flattened (Rows 2-10 from Li-yao Xia)
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
KEYWORD
nonn,tabl
AUTHOR
Li-yao Xia, Nov 02 2014
STATUS
approved