A054721 Number of 6-ary sequences with primitive period n.

1, 6, 30, 210, 1260, 7770, 46410, 279930, 1678320, 10077480, 60458370, 362797050, 2176734420, 13060694010, 78363884130, 470184976590, 2821108227840, 16926659444730, 101559946544280, 609359740010490, 3656158379595540, 21936950640097710, 131621703479470050

Offset

0,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

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

Formula

a(n) = Sum mu(d)*6^(n/d); d|n.

a(0) = 1, a(n) = n * A032164(n).

G.f.: 1 + 6 * Sum_{k>=1} mu(k) * x^k / (1 - 6*x^k). - Ilya Gutkovskiy, Apr 14 2021

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(mobius(d)*6^(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]*6^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 11 2014 *)

Crossrefs

Column k=6 of A143324.

Sequence in context: A057896 A336509 A147779 * A074111 A231209 A073087

Adjacent sequences: A054718 A054719 A054720 * A054722 A054723 A054724

Keyword

nonn

Author

N. J. A. Sloane, Apr 20 2000

Status

approved