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A296144 Number of configurations, excluding reflections and color swaps, of n beads each of four colors on a string. 3
1, 65, 7780, 1315825, 244448316, 48099214856, 9844135755168, 2074189508907945, 446932339677117580, 98028351499011470680, 21813996435165740009568, 4912693780465467348590056, 1117598703447726807428962400, 256444915320263078585645544000, 59283681793041084579875939892480, 13794224341895239072712767055117865 (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=4.
CROSSREFS
Sequence in context: A118707 A282839 A144661 * A251150 A176370 A093265
KEYWORD
nonn
AUTHOR
Marko Riedel, Dec 05 2017
STATUS
approved

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Last modified April 15 04:16 EDT 2024. Contains 371667 sequences. (Running on oeis4.)