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
Examples
Triangle starts with n=2: 2; 2, 6; 2, 12, 24; 2, 20, 72, 120; 2, 34, 180, 480, 720;
Links
- Li-yao Xia, Triangle of T(n,k) for n=2..10, k=2..n
Crossrefs
Programs
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Haskell
a n x = filter (\l -> all (< x) (zipWith (\x y -> abs (x - y)) l (tail l))) (permutations [1 .. n])
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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