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%I #19 Dec 21 2020 06:49:22
%S 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,
%T 72,80,68,60,136,148,152,72,216,116,140,116,184,408,176,404,288,412,
%U 440,356,384,464,256,704,444,812,560,348,904,800,1088,628,716,868
%N Number of rooted graceful permutations of length n.
%C 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.
%H Don Knuth, <a href="/A338986/b338986.txt">Table of n, a(n) for n = 0..173</a>
%e For n = 6 the a(6) = 12 solutions are 162534, 251643, 316254, 325164, 342516, 346152, 431625, 435261, 452613, 461523, 526134, 615243.
%Y A006967 counts all graceful permutations.
%Y If n > 2, a(n) = 4*A338988(n).
%K nonn
%O 0,3
%A _Don Knuth_, Dec 20 2020
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