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%I #6 Dec 24 2017 16:07:01
%S 1,65,7780,1315825,244448316,48099214856,9844135755168,
%T 2074189508907945,446932339677117580,98028351499011470680,
%U 21813996435165740009568,4912693780465467348590056,1117598703447726807428962400,256444915320263078585645544000,59283681793041084579875939892480,13794224341895239072712767055117865
%N Number of configurations, excluding reflections and color swaps, of n beads each of four colors on a string.
%C Power Group Enumeration applies here.
%D E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2530872/">Unique rows of pebbles</a>
%F With Z(S_{q,|m}) = [w^q] exp(Sum_{d|m} a_d w^d/d) and parameters n,k we have for nk even, (1/2) ((nk!)/k!/n!^k + (nk/2)! 2^(nk/2) [a_2^(nk/2)] Z(S_{k,|2})(Z_{n,|2}, a_2^n/n!) and for nk odd, (1/2) ((nk!)/k!/n!^k + ((nk-1)/2)! 2^((nk-1)/2) [a_1 a_2^((nk-1)/2)] Z(S_{k,|2})(Z_{n,|2}, a_2^n/n!). This sequence has k=4.
%Y Cf. A045723, A296143, A296145, A296146.
%K nonn
%O 1,2
%A _Marko Riedel_, Dec 05 2017
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