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A054720 Number of 5-ary sequences with primitive period n. 8
1, 5, 20, 120, 600, 3120, 15480, 78120, 390000, 1953000, 9762480, 48828120, 244124400, 1220703120, 6103437480, 30517574880, 152587500000, 762939453120, 3814695297000, 19073486328120, 95367421874400, 476837158124880, 2384185742187480, 11920928955078120 (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.
REFERENCES
E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.
LINKS
FORMULA
Sum mu(d)*5^(n/d); d|n.
a(0) = 1, a(n) = n * A001692(n).
G.f.: 1 + 5 * Sum_{k>=1} mu(k) * x^k / (1 - 5*x^k). - Ilya Gutkovskiy, Apr 14 2021
MAPLE
with(numtheory):
a:= n-> `if`(n=0, 1, add(mobius(d)*5^(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]*5^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Mar 11 2014 *)
CROSSREFS
Column k=5 of A143324.
Sequence in context: A028944 A332710 A352743 * A208941 A209069 A301952
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 20 2000
STATUS
approved

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Last modified April 24 14:54 EDT 2024. Contains 371960 sequences. (Running on oeis4.)