cp's OEIS Frontend

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

%I A296143 #8 Dec 24 2017 16:06:50
%S A296143 1,11,148,2955,63231,1430912,33259920,788827215,18989544145,
%T A296143 462583897776,11377251858336,282061000649064,7039841561638536,
%U A296143 176714389335432960,4457914983511649088,112945455380006673039,2872488224771372668725,73301643957476400237200,1876197202671454764901800,48152601206547990689466930
%N A296143 Number of configurations, excluding reflections and color swaps, of n beads each of three colors on a string.
%C A296143 Power Group Enumeration applies here.
%D A296143 E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.
%H A296143 Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2530872/">Unique rows of pebbles</a>
%H A296143 Marko Riedel, <a href="/A296143/a296143.maple.txt">Maple code for sequences A045723, A296143, A296144, A296145, A296146, including closed form and enumeration</a>
%F A296143 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.
%Y A296143 Cf. A045723, A296144, A296145, A296146.
%K A296143 nonn
%O A296143 1,2
%A A296143 _Marko Riedel_, Dec 05 2017