%I #21 Feb 16 2025 08:33:59
%S 12,16,0,0,168,384,0,0,4576,11808,0,0,232920,654848,0,0,16141792,
%T 48181600,0,0,1540635588,5155171200,0,0
%N Number of graceful labelings of the n-cycle graph.
%C 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
%H S. Arumugam and Jay Bagga, <a href="http://dx.doi.org/10.22342/jims.0.0.14.1-9">Graceful labeling algorithms and complexity - a survey</a>, Journal of the Indonesian Mathematical Society, Special edition, 2011, pp. 1-9.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GracefulLabeling.html">Graceful Labeling</a>
%F a(n) = 0 when n == 1 or 2 (mod 4).
%K nonn,more,changed
%O 3,1
%A _Eric W. Weisstein_, Apr 03 2020
%E 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))