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A115291
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Expansion of (1+x)^3/(1-x).
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16
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1, 4, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
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OFFSET
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0,2
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COMMENTS
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Let m=4. We observe that a(n) = Sum_{k=0..floor(n/2)} C(m,n-2*k). Then there is a link with A113311 and A040000: it is the same formula with respectively m=3 and m=2. We can generalize this result with the sequence whose G.f is given by (1+z)^(m-1)/(1-z). - Richard Choulet, Dec 08 2009
Also continued fraction expansion of (132-sqrt(17))/103. - Bruno Berselli, Sep 23 2011
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LINKS
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FORMULA
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a(n) = 8 - C(2, n) - 2*C(1, n) - 4*C(0, n);
a(n) = Sum_{k=0..n} C(3, k);
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MATHEMATICA
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CoefficientList[Series[(1+x)^3/(1-x), {x, 0, 100}], x] (* or *) PadRight[ {1, 4, 7}, 120, {8}] (* Harvey P. Dale, May 23 2016 *)
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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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