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A067334
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Convolution of Fibonacci F(n+1), n>=0, with F(n+6), n>=0.
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0
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8, 21, 50, 105, 210, 404, 758, 1395, 2530, 4535, 8052, 14184, 24820, 43185, 74770, 128901, 221382, 378940, 646690, 1100655, 1868738, 3165811, 5352360, 9032400, 15216800, 25595469, 42990578, 72110625
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n)= A067330(n+5, n) = A067418(n+5, 5) = sum(F(k+1)*F(n+6-k), k=0..n), n>=0.
a(n)= ((29*n+40)*F(n+1)+18*(n+1)*F(n))/5, with F(n) := A000045(n) (Fibonacci).
G.f.: (8+5*x)/(1-x-x^2)^2.
a(0)=8, a(1)=21, a(2)=50, a(3)=105, a(n)=2*a(n-1)+a(n-2)-2*a(n-3)- a(n-4) [From Harvey P. Dale, Apr 07 2012]
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MATHEMATICA
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CoefficientList[Series[(8+5x)/(1-x-x^2)^2, {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 1, -2, -1}, {8, 21, 50, 105}, 40] (* Harvey P. Dale, Apr 07 2012 *)
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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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