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 A090244 a(0) = 1; a(1) = 2; a(n) = { a(n-1) + a(n-2) for n even, a(n-1) - a(n-2) for n odd }. 0

%I

%S 1,2,3,1,4,3,7,4,11,7,18,11,29,18,47,29,76,47,123,76,199,123,322,199,

%T 521,322,843,521,1364,843,2207,1364,843,2207,1364,3571,2207,5778,3571,

%U 9349,5778,15127,9349,24476,15127,39603,24476,64079,39603,103682,64079

%N a(0) = 1; a(1) = 2; a(n) = { a(n-1) + a(n-2) for n even, a(n-1) - a(n-2) for n odd }.

%C Variant of Fibonacci sequence.

%C With the exception of the number 2, all numbers which occur in this sequence occur twice. The second occurrence is always 3 places after the first, e.g., a(0) = a(3) = 1; a(7) = a(10) = 7. In addition, if we take only one occurrence of each number and sort them, we get the ascending list: 1,2,3,4,7,11, ... [see A000032 or A080023].

%F G.f.: (1 + 2z + 2z^2 - z^3)/(1 - z^2 - z^4). [_Emeric Deutsch_, Jul 25 2009]

%F a(2n) = A000032(n+1) = A000204(n+1); a(2n+1) = A000032(n). [_R. J. Mathar_, Mar 22 2010]

%p G := (1+2*z+2*z^2-z^3)/(1-z^2-z^4): Gser := series(G, z = 0, 53): seq(coeff(Gser, z, n), n = 0 .. 50); # _Emeric Deutsch_, Jul 25 2009

%K easy,nonn

%O 0,2

%A Felix Tubiana (fat2(AT)columbia.edu), Jan 23 2004

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Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)