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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
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.
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
KEYWORD
nonn
AUTHOR
Don Knuth, Dec 20 2020
STATUS
approved