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A138744
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Let r_1 = 1. Let r_{m+1} = r_1 + 1/(r_2 + 1/(r_3 +...(r_{m-1} + 1/r_m)...)), a continued fraction of rational terms. Then a(n) is the sum of the (positive integer) terms in the simple continued fraction of r_n.
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2
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1, 1, 2, 4, 8, 33, 128, 109, 344, 3760, 1829, 18367, 11168, 35246, 41103, 79356, 151643, 344725, 1249071, 1678788, 5385320, 19780986, 17348076, 30966961, 85647848, 160394455, 451333739, 623813606
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OFFSET
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1,3
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COMMENTS
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This sequence is the sum of terms in the n-th row of irregular array A138742.
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LINKS
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EXAMPLE
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r_5 = 31/18, for instance, equals the simple continued fraction 1+ 1/(1 + 1/(2 + 1/(1 + 1/(1 +1/2)))). The integer terms in this continued fraction are (1,1,2,1,1,2); so a(5) = 1+1+2+1+1+2 = 8.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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