A000117 Number of even sequences with period 2n (bisection of A000011). (Formerly M1150 N0438)

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

0,2

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.

Formula

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

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 *)

Crossrefs

Cf. A000011.

Sequence in context: A006786 A125809 A245176 * A338729 A308030 A252653

Adjacent sequences: A000114 A000115 A000116 * A000118 A000119 A000120

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson, Jan 13 2000

Status

approved