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%I #10 Jun 10 2013 21:49:07
%S 1,2,3,3,5,7,10,15,22,32,47,69,101,148,217,318,466,683,1001,1467,2150,
%T 3151,4618,6768,9919,14537,21305,31224,45761,67066,98290,144051,
%U 211117,309407,453458,664575,973982,1427440,2092015,3065997,4493437,6585452,9651449
%N Number of new rationals produced at the n-th iteration by applying the map t -> {t+1, -1/t} to nonzero terms, starting with S[0] = {1}.
%C The sequence produced by repeatedly applying t->(1+t,-1/t), starting from {1} and discarding numbers produced earlier, might be called Fibonacci or rabbit ordering of the rationals, in analogy to that ordering of the positive rationals, with t -> (1+t,1/t).
%F o.g.f. = (1 + x + x^2 - x^3 - x^5)/(1 - x - x^3)
%e The terms produced as described above are (grouped by iteration, including the starting value 1 = iteration 0): [1], [2, -1], [3, -1/2, 0], [4, -1/3, 1/2], [5, -1/4, 2/3, 3/2, -2], [6, -1/5, 3/4, 5/3, -3/2, 5/2, -2/3],[7, -1/6, 4/5, 7/4, -4/3, 8/3, -3/5, 7/2, -2/5, 1/3],[8, -1/7, 5/6, 9/5, -5/4, 11/4, -4/7, 11/3, -3/8, 2/5, 9/2, -2/7, 3/5, 4/3, -3], ...
%Y Cf. A226271, A226274, A226080, A226081, A226130.
%Y Essentially (up to initial terms) the same as A003410, A058278, A097333 and, in particular, A226136.
%K nonn
%O 0,2
%A _M. F. Hasler_, Jun 01 2013