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A057198
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a(n) = (5*3^(n-1)+1)/2.
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12
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3, 8, 23, 68, 203, 608, 1823, 5468, 16403, 49208, 147623, 442868, 1328603, 3985808, 11957423, 35872268, 107616803, 322850408, 968551223, 2905653668, 8716961003, 26150883008, 78452649023, 235357947068, 706073841203, 2118221523608
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OFFSET
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1,1
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COMMENTS
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It appears that if s(n) is a first-order rational sequence of the form s(0)=4, s(n) = (2*s(n-1)+1)/(s(n-1)+2), n > 0, then s(n) = a(n)/(a(n)-1), n > 0.
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LINKS
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FORMULA
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G.f.: (5/2)*U(0) where U(k) = 1 + 2/(5*3^k + 5*3^k/(1 - 30*x*3^k/(15*x*3^k - 1/U(k+1)))); (continued fraction, 4-step). - Sergei N. Gladkovskii, Nov 01 2012
E.g.f.: (5/2)*U(0) where U(k) = 1 + 2/(5*3^k + 5*3^k/(1 - 30*x*3^k/(15*x*3^k - (k+1)/U(k+1)))); (continued fraction, 4-step). - Sergei N. Gladkovskii, Nov 01 2012
G.f.: x*(3-4*x) / ( (3*x-1)*(x-1) ). - R. J. Mathar, Jan 25 2015
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EXAMPLE
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G.f. = 3*x + 8*x^2 + 23*x^3 + 68*x^4 + 203*x^5 + 608*x^6 + 1823*x^7 + 5468*x^8 + ...
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MATHEMATICA
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Table[(5*3^(n-1) + 1)/2, {n, 30}] (* T. D. Noe, Oct 11 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Incorrect zeroth term removed by Jon Perry, Oct 11 2012
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STATUS
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approved
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