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A058082
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a(1) = 1; a(n+1) = sum of terms in continued fraction for the sum of the continued fractions, [a(1); a(2), a(3), ..., a(n)] and [0; a(1), a(2), a(3), ..., a(n)].
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1
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1, 2, 8, 18, 55, 84, 127, 146, 179, 224, 297, 548, 684, 960, 1627, 1669, 1144, 9307, 20650, 2234, 3977, 2311, 2393, 2523, 4949, 2856, 3118, 11000, 3324, 3230, 3084, 3555, 4173, 3936, 7738, 3786, 4472, 4491, 5188, 4100, 4849, 4674, 6089, 4955, 5862
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OFFSET
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1,2
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LINKS
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EXAMPLE
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[a(1); a(2)] + [0; a(1), a(2)] = 13/6 = [2; 6]. So a(3) = 2 + 6 = 8.
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MAPLE
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A[1]:= 1: v:= 1: P:= <<1, 0>|<0, 1>>:
for n from 2 to 100 do
P:= P . <<v, 1>|<1, 0>>;
t:= P[1, 1]/P[2, 1];
v:=convert(numtheory:-cfrac(t+1/t, `quotients`), `+`);
A[n]:= v;
od:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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