

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
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OFFSET

1,2


LINKS



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())


CROSSREFS



KEYWORD

nonn,easy,changed


AUTHOR



EXTENSIONS



STATUS

approved



