The OEIS is supported by the many generous donors to the OEIS Foundation.
%I M1150 N0438 #33 Jun 26 2022 04:14:55
%S 1,2,4,8,18,44,122,362,1162,3914,13648,48734,176906,649532,2405236,
%T 8964800,33588234,126390032,477353376,1808676326,6872485104,
%U 26179922024,99957747388,382443112538,1466024067850,5629516646996,21651955485304,83400061453514
%N Number of even sequences with period 2n (bisection of A000011).
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A000117/b000117.txt">Table of n, a(n) for n = 0..500</a>
%H E. N. Gilbert and J. Riordan, <a href="http://projecteuclid.org/euclid.ijm/1255631587">Symmetry types of periodic sequences</a>, Illinois J. Math., 5 (1961), 657-665.
%F a(n) ~ 4^(n-1) / (2*n). - _Cedric Lorand_, Apr 18 2022
%t b[0] = 1; b[n_] := (2^Floor[n/2] + (Table[EulerPhi[2d]*2^(n/d)/(2n), {d, Divisors[n]}] // Accumulate // Last))/2; a[n_] := b[2n]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 07 2014 *)
%Y Cf. A000011.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_, Jan 13 2000