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A276505
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Number of rational numbers > 1 whose numerator in reduced form equals n and that can be written as a continued fraction with exactly three partial quotients.
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0
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0, 0, 1, 1, 3, 1, 5, 2, 5, 3, 7, 2, 9, 3, 6, 6, 11, 1, 11, 4, 9, 7, 11, 4, 13, 5, 9, 6, 15, 3, 17, 6, 10, 7, 12, 6, 19, 7, 9, 7, 19, 4, 17, 8, 11, 11, 17, 3, 21, 5, 14, 10, 17, 5, 19, 11, 17, 9, 17, 4, 21, 9, 10, 12, 21, 7, 23, 8, 16, 7, 25, 7, 25, 7, 7, 14
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OFFSET
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1,5
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COMMENTS
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Equivalently, this is the number of solutions of the equation n = xyz + x + z in positive integer x, y and z.
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LINKS
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EXAMPLE
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For n=5 there are three rational numbers which satisfy all the conditions: 5/2 = [2;1,1], 5/3 = [1;1,2] and 5/4 = [1;3,1]. Therefore a(5) = 3.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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