|
|
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.
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))):
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|