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A054718 Number of ternary sequences with primitive period n. 8
1, 3, 6, 24, 72, 240, 696, 2184, 6480, 19656, 58800, 177144, 530640, 1594320, 4780776, 14348640, 43040160, 129140160, 387400104, 1162261464, 3486725280, 10460350992, 31380882456, 94143178824, 282428998560, 847288609200, 2541864234000, 7625597465304 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equivalently, output sequences with primitive period n from a simple cycling shift register.

Column k=3 of A143324.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2095 (terms 0..650 from Alois P. Heinz)

E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.

FORMULA

a(n) = Sum_{d|n} mu(d)*3^(n/d).

a(0) = 1, a(n) = n * A027376(n).

a(n) = 3 * A034741(n).

MAPLE

with(numtheory):

a:= n-> `if`(n=0, 1, add(mobius(d)*3^(n/d), d=divisors(n))):

seq(a(n), n=0..30);  # Alois P. Heinz, Oct 21 2012

MATHEMATICA

a[0] = 1; a[n_] := Sum[MoebiusMu[d]*3^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Mar 11 2014, after Alois P. Heinz *)

PROG

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(d) * 3^(n/d) )); \\ Joerg Arndt, Apr 14 2013

CROSSREFS

Cf. A027375, A054719, A054720, A054721.

Sequence in context: A148655 A148656 A279300 * A132390 A327643 A296215

Adjacent sequences:  A054715 A054716 A054717 * A054719 A054720 A054721

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 20 2000

STATUS

approved

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Last modified October 19 11:26 EDT 2019. Contains 328216 sequences. (Running on oeis4.)