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A296143
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Number of configurations, excluding reflections and color swaps, of n beads each of three colors on a string.
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4
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1, 11, 148, 2955, 63231, 1430912, 33259920, 788827215, 18989544145, 462583897776, 11377251858336, 282061000649064, 7039841561638536, 176714389335432960, 4457914983511649088, 112945455380006673039, 2872488224771372668725, 73301643957476400237200, 1876197202671454764901800, 48152601206547990689466930
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OFFSET
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1,2
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COMMENTS
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Power Group Enumeration applies here.
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REFERENCES
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E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.
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LINKS
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FORMULA
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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=3.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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