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 A000208 Number of even sequences with period 2n. (Formerly M2377 N0943) 3
 1, 1, 3, 4, 12, 28, 94, 298, 1044, 3658, 13164, 47710, 174948, 645436, 2397342, 8948416, 33556500, 126324496, 477225962, 1808414182, 6871973952, 26178873448, 99955697946, 382438918234, 1466015854100, 5629499869780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 Vincenzo Librandi, 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(n) = (A000013(2*n)+A000013(n))/2 if n even, A000013(2*n)/2 if n odd. - Randall L. Rathbun, Jan 11 2002 a(2*n) = (A000116(2*n) + A000116(n)) / 2; a(2*n+1) = A000116(2*n+1) / 2. - Reinhard Zumkeller, Jul 08 2013 MATHEMATICA a[0] = 1; a13[0] = 1; a13[n_] := Fold[#1 + EulerPhi[2*#2]*(2^(n/#2)/(2*n)) & , 0, Divisors[n]]; a[(n_)?OddQ] := (a13[2*(n + 1)] + a13[n + 1])/2; a[(n_)?EvenQ] := a13[2*(n + 1)]/2; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Sep 01 2011, after PARI prog. *) PROG (PARI) {A000208(n)=if(n%2==0, (A000013(2*n)+A000013(n))/2, A000013(2*n)/2)} (Haskell) a000208 n = a000208_list !! n a000208_list = map (`div` 2) \$ concat \$ transpose    [zipWith (+) a000116_list \$ bis a000116_list, bis \$ tail a000116_list]    where bis (x:_:xs) = x : bis xs -- Reinhard Zumkeller, Jul 08 2013 CROSSREFS Cf. A000013, A000206. Sequence in context: A288140 A287594 A296271 * A079154 A101716 A217477 Adjacent sequences:  A000205 A000206 A000207 * A000209 A000210 A000211 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Randall L. Rathbun, Jan 11 2002 STATUS approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)