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A140660
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a(n) = 3*4^n + 1.
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8
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4, 13, 49, 193, 769, 3073, 12289, 49153, 196609, 786433, 3145729, 12582913, 50331649, 201326593, 805306369, 3221225473, 12884901889, 51539607553, 206158430209, 824633720833, 3298534883329, 13194139533313, 52776558133249
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OFFSET
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0,1
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COMMENTS
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An Engel expansion of 4/3 to the base 4 as defined in A181565, with the associated series expansion 4/3 = 4/4 + 4^2/(4*13) + 4^3/(4*13*49) + 4^4/(4*13*49*193) + .... Cf. A199115. - Peter Bala, Oct 29 2013
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 3.
First differences: a(n+1) - a(n) = A002063(n).
O.g.f.: (7*x - 4)/((1 - x)*(4*x - 1)). - R. J. Mathar, Jul 14 2008
E.g.f.: 3*exp(4*x) + exp(x).
a(n) = 5*a(n-1) - 4*a(n-2). (End)
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MATHEMATICA
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LinearRecurrence[{5, -4}, {4, 13}, 50] (* or *) CoefficientList[Series[ (7*x-4)/((1-x)*(4*x-1)), {x, 0, 50}], x] (* G. C. Greubel, Sep 15 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec((7*x-4)/((1-x)*(4*x-1))) \\ G. C. Greubel, Sep 15 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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