A338986 Number of rooted graceful permutations of length n.

1, 1, 2, 4, 4, 8, 12, 4, 12, 12, 16, 20, 28, 12, 12, 60, 16, 20, 40, 48, 48, 52, 44, 76, 52, 72, 80, 68, 60, 136, 148, 152, 72, 216, 116, 140, 116, 184, 408, 176, 404, 288, 412, 440, 356, 384, 464, 256, 704, 444, 812, 560, 348, 904, 800, 1088, 628, 716, 868

Offset

0,3

Comments

A permutation p[1]...p[n] of {1,...n} is graceful if the n-1 differences |p[j+1] -p[j]| are distinct. It is rooted if, in addition, |p[j+1] - p[j]| = k < n-1 implies that either |p[j] - p[j-1]| > k or |p[j+2] - p[j+1]| > k.

Links

Don Knuth, Table of n, a(n) for n = 0..173

Example

For n = 6 the a(6) = 12 solutions are 162534, 251643, 316254, 325164, 342516, 346152, 431625, 435261, 452613, 461523, 526134, 615243.

Crossrefs

A006967 counts all graceful permutations.

If n > 2, a(n) = 4*A338988(n).

Sequence in context: A227333 A223317 A027131 * A319803 A055946 A130124

Adjacent sequences: A338983 A338984 A338985 * A338987 A338988 A338989

Keyword

nonn

Author

Don Knuth, Dec 20 2020

Status

approved