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A154251
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Expansion of (1-x+7x^2)/((1-x)(1-2x)).
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4
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1, 2, 11, 29, 65, 137, 281, 569, 1145, 2297, 4601, 9209, 18425, 36857, 73721, 147449, 294905, 589817, 1179641, 2359289, 4718585, 9437177, 18874361, 37748729, 75497465, 150994937, 301989881, 603979769, 1207959545, 2415919097
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OFFSET
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0,2
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COMMENTS
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Binomial transform of 1,1,8,1,8,1,8,1,8,1,8,1,8,1,8,...
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 2*a(n-2), n>2, with a(0)=1, a(1)=2, a(2)=11.
a(n) = 9*2^(n-1) - 7, n>0, with a(0)=1.
a(n) = 2*a(n-1) + 7, n>1, with a(0)=1, a(1)=2.
a(n) = 9*2^(n-1) - 7 for n >= 1.
E.g.f.: (1/2)*(9*exp(2*x) - 14*exp(x) + 7). (End)
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MATHEMATICA
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Join[{1}, LinearRecurrence[{3, -2}, {2, 11}, 25]] (* or *) Join[{1}, Table[9*2^(n-1) - 7, {n, 1, 25}]] (* G. C. Greubel, Sep 08 2016 *)
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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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STATUS
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approved
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