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 A228805 Number of distinct denominators of rational numbers whose continued fraction consists exclusively of 1s and 2s and has length <=n. 2
 1, 2, 4, 8, 14, 26, 45, 85, 155, 286, 540, 1047, 2014, 3939, 7642, 15082, 29601, 58797, 116248, 231530, 459976, 917030, 1826669, 3641525, 7253511, 14463688, 28834305, 57481793, 114543879, 228286471 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..30. EXAMPLE a = 1 counts the denominators in {1/1,2/1} corresponding to the continued fractions [1] and [2]; a(2) = 2 counts the denominators in {1/1,2/1,2/1,3/2,3/1,5/2} corresponding to the continued fractions [1], [2], [1,1], [1,2], [2,1], [2,2]. MATHEMATICA a[n_] := Length[Sort[Union[Denominator[Map[FromContinuedFraction, Flatten[Map[Tuples[{1, 2}, #] &, Range[n]], 1]]]]]]; Table[a[n], {n, 1, 12}] PROG (Sage) import itertools def a(n): ans = set() for k in range(1, n+1): for p in itertools.product([1, 2], repeat=k): ans.add(continued_fraction(p).value().denominator()) return len(ans) # Robin Visser, Nov 19 2023 CROSSREFS Cf. A228803. Sequence in context: A027557 A120545 A130708 * A317884 A365253 A054193 Adjacent sequences: A228802 A228803 A228804 * A228806 A228807 A228808 KEYWORD nonn,easy,changed AUTHOR Clark Kimberling, Sep 04 2013 EXTENSIONS a(23)-a(30) from Robin Visser, Nov 19 2023 STATUS approved

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Last modified December 2 03:27 EST 2023. Contains 367505 sequences. (Running on oeis4.)