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

1, 5363, 95304160, 2254635672135, 61689337799825736, 1854290094982330189184, 59529536963190914931717120, 2006426039057377710970239751995, 70206501544183654687465441723567000, 2530662094366411886472214155427418011488, 93449587615256254621892607439280048712775680

Offset

1,2

Comments

Power Group Enumeration applies here.

References

E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.

Links

Table of n, a(n) for n=1..11.

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=6.

Crossrefs

Cf. A045723, A296143, A296144, A296145.

Sequence in context: A145770 A258074 A237295 * A063408 A057850 A058325

Adjacent sequences: A296143 A296144 A296145 * A296147 A296148 A296149

Keyword

nonn

Author

Marko Riedel, Dec 05 2017

Status

approved