%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(n1) + a(n2) for n even, a(n1)  a(n2) 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^2z^3)/(1z^2z^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
