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A256217 a(n) = A000011(n) - A256216(n). 9
1, 2, 2, 4, 4, 7, 8, 14, 16, 26, 32, 52, 64, 101, 128, 202, 256, 399, 512, 796, 1024, 1583, 2048, 3162, 4096, 6302, 8192, 12586, 16384, 25124, 32768, 50186, 65536, 100232, 131072, 200266, 262144, 400115, 524288, 799568, 1048576, 1597834, 2097152, 3193438, 4194304, 6382637, 8388608, 12757770, 16777216, 25501370 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Counts contiguously substituted cycloalkane polyols (CSCPs).
Consider a bracelet of n beads, each colored blue on one side and red on the other -- each bead changes color when the bracelet is turned over. Reversal is then the same as swapping the colors. a(n) is the number of colorings that are invariant under reversal, up to rotation and turning over. - Ed Wynn, May 22 2021
LINKS
Shinsaku Fujita, alpha-beta Itemized Enumeration of Inositol Derivatives and m-Gonal Homologs by Extending Fujita's Proligand Method, Bull. Chem. Soc. Jpn. 2017, 90, 343-366; doi:10.1246/bcsj.20160369. See Table 8.
A. Yajima, How to calculate the number of stereoisomers of inositol-homologs, Bull. Chem. Soc. Jpn. 2014, 87, 1260-1264 | doi:10.1246/bcsj.20140204. See Table 2 (M_c).
FORMULA
a(n) = A056503(n) for odd n. - Andrew Howroyd, Jun 14 2021
EXAMPLE
The a(7) = 8 bracelets are rrrrrrr, rrrrrrb, rrrrrbb, rrrrbbb, rrrrbrb, rrrbrrb, rrbbrrb, rrbrbrb. - Ed Wynn, May 22 2021
a(12) = A056503(12) + 1. The extra bracelet is rrrbrrbbbrbb. - Andrew Howroyd, Jun 25 2021
CROSSREFS
The 8 sequences in Table 8 of Fujita (2017) are A053656, A000011, A256216, A256217, A123045, A283846, A283847, A283848.
Sequence in context: A005308 A151532 A056503 * A361439 A055636 A206559
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 26 2015
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)