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 A296146 Number of configurations, excluding reflections and color swaps, of n beads each of six colors on a string. 3

%I

%S 1,5363,95304160,2254635672135,61689337799825736,

%T 1854290094982330189184,59529536963190914931717120,

%U 2006426039057377710970239751995,70206501544183654687465441723567000,2530662094366411886472214155427418011488,93449587615256254621892607439280048712775680

%N Number of configurations, excluding reflections and color swaps, of n beads each of six 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=6.

%Y Cf. A045723, A296143, A296144, A296145.

%K nonn

%O 1,2

%A _Marko Riedel_, Dec 05 2017

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)