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A296143 Number of configurations, excluding reflections and color swaps, of n beads each of three colors on a string. 4
1, 11, 148, 2955, 63231, 1430912, 33259920, 788827215, 18989544145, 462583897776, 11377251858336, 282061000649064, 7039841561638536, 176714389335432960, 4457914983511649088, 112945455380006673039, 2872488224771372668725, 73301643957476400237200, 1876197202671454764901800, 48152601206547990689466930 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Power Group Enumeration applies here.
REFERENCES
E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.
LINKS
Marko Riedel et al., Unique rows of pebbles
FORMULA
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.
CROSSREFS
Sequence in context: A093750 A194726 A367790 * A217722 A261536 A175635
KEYWORD
nonn
AUTHOR
Marko Riedel, Dec 05 2017
STATUS
approved

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Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)