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A338986 Number of rooted graceful permutations of length n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 21:06 EST 2022. Contains 350515 sequences. (Running on oeis4.)