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 A296145 Number of configurations, excluding reflections and color swaps, of n beads each of five colors on a string. 3
 1, 513, 701260, 1273147785, 2597337494136, 5711975829039480, 13239412829570653440, 31902976888441563215025, 79210992511055955027177700, 201394898991255834414075013488, 522024491776928458970588283023040, 1374924298868439440732405164346591160, 3670434093979203432106449568933449100800, 9911788665178411118992936004423729374579200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Power Group Enumeration applies here. 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=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

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)