A000117 Number of even sequences with period 2n (bisection of A000011).

1, 2, 4, 8, 18, 44, 122, 362, 1162, 3914, 13648, 48734, 176906, 649532, 2405236, 8964800, 33588234, 126390032, 477353376, 1808676326, 6872485104, 26179922024, 99957747388, 382443112538, 1466024067850, 5629516646996, 21651955485304, 83400061453514

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.

Crossrefs

Cf. A000011.

Programs

Mathematica

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 *)

Formula

a(n) ~ 4^(n-1) / (2*n). - Cedric Lorand, Apr 18 2022

Extensions

More terms from David W. Wilson, Jan 13 2000