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A253076 Bisection of A136704. 3
1, 5, 30, 205, 1476, 11070, 85410, 672605, 5380830, 43584804, 356602950, 2941974270, 24441017580, 204257075490, 1715759433624, 14476720225405, 122626336026960, 1042323856225470, 8887182353111790, 75985409119105764, 651303506735164140, 5595289216952336550 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A sequence in Table 1 of Hao (1991) appears to match this sequence, but there are not enough terms there to be certain. It is possible that Hao's 1989 book will clarify things, but I do not have access to it.

REFERENCES

Hao, Bai Lin, Elementary symbolic dynamics and chaos in dissipative systems. World Scientific Publishing Co., Inc., Teaneck, NJ, 1989. xvi+460 pp. ISBN: 9971-50-682-3; 9971-50-698-X

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Bai-lin Hao, Symbolic dynamics and characterization of complexity, Physica, D51 (1991), 161-176.

FORMULA

a(n) = (1/8*n) * Sum_{d|n, d odd} mu(d)*(3^(2*n/d) - 1). - Andrew Howroyd, Nov 11 2018

MATHEMATICA

a[n_] := Sum[Boole[OddQ[d]] MoebiusMu[d] (3^(2n/d)-1), {d, Divisors[n]}]/(8n);

Array[a, 22] (* Jean-Fran├žois Alcover, Aug 26 2019 *)

PROG

(PARI) a(n) = sumdiv(n>>valuation(n, 2), d, moebius(d)*(3^(2*n/d)-1))/(8*n); \\ Andrew Howroyd, Nov 11 2018

CROSSREFS

Cf. A136704, A253077.

Sequence in context: A118346 A234422 A091927 * A165312 A082301 A144180

Adjacent sequences:  A253073 A253074 A253075 * A253077 A253078 A253079

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 01 2015

EXTENSIONS

Offset corrected and terms a(14) and beyond from Andrew Howroyd, Nov 11 2018

STATUS

approved

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Last modified October 23 14:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)