A253076 Bisection of A136704.

1, 5, 30, 205, 1476, 11070, 85410, 672605, 5380830, 43584804, 356602950, 2941974270, 24441017580, 204257075490, 1715759433624, 14476720225405, 122626336026960, 1042323856225470, 8887182353111790, 75985409119105764, 651303506735164140, 5595289216952336550

Offset: 1

Author

N. J. A. Sloane, Feb 01 2015

Keywords

• nonn

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.

Crossrefs

Cf. A136704, A253077.

Programs

Mathematica

a[n_] := Sum[Boole[OddQ[d]] MoebiusMu[d] (3^(2n/d)-1), {d, Divisors[n]}]/(8n);
Array[a, 22] (* Jean-François Alcover, Aug 26 2019 *)

PARI

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

Formula

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

Extensions

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