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A333720
Number of graceful labelings of the n-cycle graph.
0
12, 16, 0, 0, 168, 384, 0, 0, 4576, 11808, 0, 0, 232920, 654848, 0, 0, 16141792, 48181600, 0, 0, 1540635588, 5155171200, 0, 0
OFFSET
3,1
COMMENTS
In the paper by Arumugam and Bagga, the number of graceful labelings of the n-cycle graph with label m missing (and with the labels 0 and n at given neighboring vertices) is computed. Summing over m, they obtain a(n)/(2*n). In Table 3.2 in the paper, however, the sum of the terms does not equal the total for n = 16 and n = 23. For n = 23, it is obvious that (at least) one term is incorrect, as the terms for m = 11 and m = 12 should be equal but are given as 5252774 and 5253774. The terms given here are based on the totals. - Pontus von Brömssen, Aug 06 2020
LINKS
S. Arumugam and Jay Bagga, Graceful labeling algorithms and complexity - a survey, Journal of the Indonesian Mathematical Society, Special edition, 2011, pp. 1-9.
Eric Weisstein's World of Mathematics, Cycle Graph
Eric Weisstein's World of Mathematics, Graceful Labeling
FORMULA
a(n) = 0 when n == 1 or 2 (mod 4).
CROSSREFS
Sequence in context: A079322 A167304 A191966 * A135451 A175784 A143090
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Apr 03 2020
EXTENSIONS
a(15) to a(26) from Pontus von Brömssen, Aug 06 2020 (taken from Table 3.2 in the paper by Arumugam and Bagga, expressed there as a(n)/(2*n))
STATUS
approved