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A283847 Number of n-gonal inositol homologs with 2 kinds of achiral proligands. 9
2, 8, 36, 140, 522, 1920, 7030, 25704, 94302, 347488, 1286460, 4785300, 17879352, 67076096, 252579600, 954306220, 3616552422, 13743371072, 52356648380, 199909107900, 764873459802, 2932022620160, 11258982291252 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Robert Israel, Table of n, a(n) for n = 3..1665

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.

FORMULA

From Robert Israel, Aug 23 2018 after Fujita (2017), Eq. (100)(set n=2, m=n): (Start)

if n is even, a(n) = (4*n)^(-1)*(Sum_{d|n, d odd} phi(d)*4^(n/d) - 2^(n-1).

if n is odd, a(n) = (4*n)^(-1)*Sum_{d|n} phi(d)*4^(n/d) - 2^(n-1). (End)

MAPLE

f:= proc(n) uses numtheory;

  if n::even then (4*n)^(-1)*add(phi(d)*4^(n/d), d = select(type, divisors(n), odd)) - 2^(n-1)

  else (4*n)^(-1)*add(phi(d)*4^(n/d), d = divisors(n)) - 2^(n-1)

  fi

end proc:

map(f, [$3..50]); # Robert Israel, Aug 23 2018

MATHEMATICA

a[n_] := If[EvenQ[n], (4n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Select[ Divisors[n], OddQ]}] - 2^(n-1), (4n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Divisors[n]}] - 2^(n-1)];

Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Mar 23 2019, after Robert Israel *)

CROSSREFS

The 8 sequences in Table 8 of Fujita (2017) are A053656, A000011, A256216, A256217, A123045, A283846, A283847, A283848.

Sequence in context: A248861 A323677 A295501 * A123290 A321110 A228791

Adjacent sequences:  A283844 A283845 A283846 * A283848 A283849 A283850

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 01 2017

STATUS

approved

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Last modified April 18 14:35 EDT 2019. Contains 322209 sequences. (Running on oeis4.)