A296145 Number of configurations, excluding reflections and color swaps, of n beads each of five colors on a string.

1, 513, 701260, 1273147785, 2597337494136, 5711975829039480, 13239412829570653440, 31902976888441563215025, 79210992511055955027177700, 201394898991255834414075013488, 522024491776928458970588283023040, 1374924298868439440732405164346591160, 3670434093979203432106449568933449100800, 9911788665178411118992936004423729374579200

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..14.

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=5.

Crossrefs

Cf. A045723, A296143, A296144, A296146.

Sequence in context: A094647 A236431 A118709 * A283369 A103351 A291507

Adjacent sequences: A296142 A296143 A296144 * A296146 A296147 A296148

Keyword

nonn

Author

Marko Riedel, Dec 05 2017

Status

approved