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A283848 Number of n-gonal inositol homologs with 2 kinds of achiral proligands. 9
8, 23, 32, 86, 128, 339, 512, 1332, 2048, 5298, 8192, 21066, 32768, 83987, 131072, 334966, 524288, 1336988, 2097152, 5338206, 8388608, 21321234, 33554432, 85176636, 134217728, 340338398, 536870912, 1360073016, 2147483648, 5435820051, 8589934592, 21727481616, 34359738368, 86853790498, 137438953472 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Robert Israel, Table of n, a(n) for n = 3..3318

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

If n is even, a(n) = (2*n)^(-1)*Sum_{d|n, d even} phi(d)*4^(n/d) + 5*2^(n-2). - Robert Israel, Aug 23 2018 after Fujita (2017), Eq. (101) (set n=2, m=n).

If n is odd, a(n) = 2^n. For the even bisection see A284711.

MAPLE

f:= proc(n) uses numtheory;

  if n::even then (2*n)^(-1)*add(phi(d)*4^(n/d), d=select(type, divisors(n), even))+5*2^(n-2)

  else 2^n

  fi

end proc:

map(f, [$1..40]); # Robert Israel, Aug 23 2018

MATHEMATICA

a[n_] := If[EvenQ[n], (2n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Select[ Divisors[n], EvenQ]}] + 5*2^(n-2), 2^n];

Table[a[n], {n, 3, 40}] (* Jean-Fran├žois Alcover, Mar 23 2019, after Robert Israel *)

PROG

(PARI) a(n) = if (n%2, 2^n, (2*n)^(-1)*sumdiv(n, d, if (!(d%2), eulerphi(d)*4^(n/d))) + 5*2^(n-2)); \\ Michel Marcus, Mar 23 2019

CROSSREFS

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

Sequence in context: A029755 A022420 A034811 * A287167 A253975 A003342

Adjacent sequences:  A283845 A283846 A283847 * A283849 A283850 A283851

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 01 2017

EXTENSIONS

Edited and more terms by Robert Israel, Aug 23 2018

STATUS

approved

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Last modified April 22 06:14 EDT 2019. Contains 322329 sequences. (Running on oeis4.)