A296143 Number of configurations, excluding reflections and color swaps, of n beads each of three colors on a string.

1, 11, 148, 2955, 63231, 1430912, 33259920, 788827215, 18989544145, 462583897776, 11377251858336, 282061000649064, 7039841561638536, 176714389335432960, 4457914983511649088, 112945455380006673039, 2872488224771372668725, 73301643957476400237200, 1876197202671454764901800, 48152601206547990689466930

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..20.

Marko Riedel et al., Unique rows of pebbles

Marko Riedel, Maple code for sequences A045723, A296143, A296144, A296145, A296146, including closed form and enumeration

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

Cf. A045723, A296144, A296145, A296146.

Sequence in context: A093750 A194726 A367790 * A217722 A261536 A175635

Adjacent sequences: A296140 A296141 A296142 * A296144 A296145 A296146

Keyword

nonn

Author

Marko Riedel, Dec 05 2017

Status

approved