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A283846 Number of n-gonal inositol homologs with 2 kinds of achiral proligands. 9
10, 31, 68, 226, 650, 2259, 7542, 27036, 96350, 352786, 1294652, 4806366, 17912120, 67160083, 252710672, 954641186, 3617076710, 13744708060, 52358745532, 199914446106, 764881848410, 2932043941394, 11259015845684 (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 21 2018 after Fujita (2017), Eq. (99)(set n=2, m=n): (Start)

if n is even, a(n) = (4*n)^(-1)*(Sum_{d|n} phi(d)*4^(n/d) + Sum_{d|n, d even} phi(d)*4^(n/d)) + 3*2^(n-2).

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

MAPLE

f:=  proc(m) uses numtheory;

  if m::even then 1/(4*m)*add(phi(d)*4^(m/d)*`if`(d::even, 2, 1), d = divisors(m))

+ 3*2^(m-2)

  else

1/(4*m)*add(phi(d)*4^(m/d), d=divisors(m))+2^(m-1)

  fi

end proc:

map(f, [$3..100]); # Robert Israel, Aug 21 2018

MATHEMATICA

f[m_] := If[EvenQ[m], 1/(4m)*Sum[EulerPhi[d]*4^(m/d)*If[EvenQ[d], 2, 1], {d, Divisors[m]}]+ 3*2^(m-2), 1/(4m)*Sum[EulerPhi[d]*4^(m/d), {d, Divisors[m]}] + 2^(m-1)];

f /@ Range[3, 25] (* Jean-Fran├žois Alcover, Feb 26 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: A192023 A219693 A297507 * A163655 A041190 A111500

Adjacent sequences:  A283843 A283844 A283845 * A283847 A283848 A283849

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 01 2017

STATUS

approved

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Last modified April 19 16:58 EDT 2019. Contains 322283 sequences. (Running on oeis4.)