OFFSET
0,2
COMMENTS
Equivalently, output sequences with primitive period n from a simple cycling shift register.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1660 (terms 0..500 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)*4^(n/d).
a(n) = n * A027377(n), n>0.
G.f.: 1 + 4 * Sum_{k>=1} mu(k) * x^k / (1 - 4*x^k). - Ilya Gutkovskiy, Apr 14 2021
MAPLE
A054719 := proc(n) local d, s; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+mobius(d)*4^(n/d); od; RETURN(s); fi; end;
MATHEMATICA
a[0] = 1; a[n_] := Sum[MoebiusMu[d]*4^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 11 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 20 2000
STATUS
approved