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A000116 Number of even sequences with period 2n (bisection of A000013).
(Formerly M1156 N0440)
4
1, 2, 4, 8, 20, 56, 180, 596, 2068, 7316, 26272, 95420, 349716, 1290872, 4794088, 17896832, 67110932, 252648992, 954444608, 3616828364, 13743921632, 52357746896, 199911300472, 764877836468, 2932031358484, 11258999739560, 43303843861744, 166799988689300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(2*n) + a(n) = 2 * A000208(2*n); a(2*n+1) = 2 * A000208(2*n+1). - Reinhard Zumkeller, Jul 08 2013

REFERENCES

E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.

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

MAPLE

with (numtheory):

a:= n-> `if`(n=0, 1, add (phi(2*d) *2^(2*n/d), d=divisors(2*n))/(4*n)):

seq (a(n), n=0..20); # Alois P. Heinz, Mar 25 2012

MATHEMATICA

a[n_] := Sum[ EulerPhi[2d]*2^(2n/d), {d, Divisors[2n]}]/(4n); a[0]=1; Table[a[n], {n, 0, 27}] (* Jean-Fran├žois Alcover, Sep 13 2012, after Alois P. Heinz *)

PROG

(Haskell)

a000116 n = a000116_list !! n

a000116_list = bis a000013_list where bis (x:_:xs) = x : bis xs

-- Reinhard Zumkeller, Jul 08 2013

CROSSREFS

Cf. A000013, A026119.

Sequence in context: A123611 A082279 A113180 * A302862 A006407 A100447

Adjacent sequences:  A000113 A000114 A000115 * A000117 A000118 A000119

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson, Jan 13 2000

STATUS

approved

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Last modified May 30 08:04 EDT 2020. Contains 334712 sequences. (Running on oeis4.)