A296144 Number of configurations, excluding reflections and color swaps, of n beads each of four colors on a string.
1, 65, 7780, 1315825, 244448316, 48099214856, 9844135755168, 2074189508907945, 446932339677117580, 98028351499011470680, 21813996435165740009568, 4912693780465467348590056, 1117598703447726807428962400, 256444915320263078585645544000, 59283681793041084579875939892480, 13794224341895239072712767055117865
Offset: 1
Keywords
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.
Comments