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%I #46 Jul 04 2021 16:11:08
%S 1,2,2,4,4,7,8,14,16,26,32,52,64,101,128,202,256,399,512,796,1024,
%T 1583,2048,3162,4096,6302,8192,12586,16384,25124,32768,50186,65536,
%U 100232,131072,200266,262144,400115,524288,799568,1048576,1597834,2097152,3193438,4194304,6382637,8388608,12757770,16777216,25501370
%N a(n) = A000011(n) - A256216(n).
%C Counts contiguously substituted cycloalkane polyols (CSCPs).
%C 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
%H Seiichi Manyama, <a href="/A256217/b256217.txt">Table of n, a(n) for n = 1..6644</a>
%H Shinsaku Fujita, <a href="https://www.webfile.jp/lite-tcsj/dl.php?i=2071&s=aaa3068608b595219b60">alpha-beta Itemized Enumeration of Inositol Derivatives and m-Gonal Homologs by Extending Fujita's Proligand Method</a>, Bull. Chem. Soc. Jpn. 2017, 90, 343-366; doi:10.1246/bcsj.20160369. See Table 8.
%H A. Yajima, <a href="https://www.jstage.jst.go.jp/article/bcsj/87/11/87_20140204/_pdf">How to calculate the number of stereoisomers of inositol-homologs</a>, Bull. Chem. Soc. Jpn. 2014, 87, 1260-1264 | doi:10.1246/bcsj.20140204. See Table 2 (M_c).
%F a(n) = A056503(n) for odd n. - _Andrew Howroyd_, Jun 14 2021
%e The a(7) = 8 bracelets are rrrrrrr, rrrrrrb, rrrrrbb, rrrrbbb, rrrrbrb, rrrbrrb, rrbbrrb, rrbrbrb. - _Ed Wynn_, May 22 2021
%e a(12) = A056503(12) + 1. The extra bracelet is rrrbrrbbbrbb. - _Andrew Howroyd_, Jun 25 2021
%Y Cf. A000011, A053656, A056503, A066314, A256216.
%Y The 8 sequences in Table 8 of Fujita (2017) are A053656, A000011, A256216, A256217, A123045, A283846, A283847, A283848.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Mar 26 2015
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