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A000208
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Number of even sequences with period 2n.
(Formerly M2377 N0943)
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2
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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; internal format)
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OFFSET
| 0,3
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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).
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FORMULA
| a(n) = (A000013(2*n)+A000013(n))/2 if n odd or A000013(2*n)/2 if n even.
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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}] (* From Jean-François Alcover, Sep 01 2011, after PARI prog. *)
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PROG
| (PARI) {A000208(n)=if(n%2==0, (A000013(2*n)+A000013(n))/2, A000013(2*n)/2)}
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CROSSREFS
| Cf. A000013, A000206.
Sequence in context: A002986 A147569 A090660 * A079154 A101716 A109771
Adjacent sequences: A000205 A000206 A000207 * A000209 A000210 A000211
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and formula from Randall L. Rathbun, Jan 11 2002
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