A256217 a(n) = A000011(n) - A256216(n).

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

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

Seiichi Manyama, Table of n, a(n) for n = 1..6644

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

Cf. A000011, A053656, A056503, A066314, A256216.

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

Adjacent sequences: A256214 A256215 A256216 * A256218 A256219 A256220

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2015

Status

approved