A338988 -id:A338988 - cp's OEIS frontend

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

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Don Knuth, Dec 20 2020

nonn

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.

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

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

A006967 counts all graceful permutations.

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

cp's OEIS Frontend

A338986 Number of rooted graceful permutations of length n.

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