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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 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..1000 E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665. FORMULA a(2*n) + a(n) = 2 * A000208(2*n); a(2*n+1) = 2 * A000208(2*n+1). - Reinhard Zumkeller, Jul 08 2013 a(n) ~ 4^(n-1) / n. - Cedric Lorand, Apr 18 2022 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-François 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 A344490 A006407 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 August 7 01:21 EDT 2024. Contains 375002 sequences. (Running on oeis4.)