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A073378
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Eighth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.
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3
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1, 9, 63, 345, 1665, 7227, 29073, 109791, 394020, 1354210, 4486482, 14397318, 44932446, 136817370, 407566350, 1190446866, 3415935699, 9645169743, 26836557825, 73670997015, 199751003991, 535449185469
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OFFSET
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0,2
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (9,-18,-60,234,126,-1176,36,3519,-479,-7038,144, 9408,2016,-7488,-3840,2304,2304,512).
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FORMULA
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a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073377(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+8, 8) * binomial(n-k, k) * 2^k.
G.f.: 1/(1-(1+2*x)*x)^9 = 1/((1+x)*(1-2*x))^9.
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MATHEMATICA
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CoefficientList[Series[1/((1+x)*(1-2*x))^9, {x, 0, 40}], x] (* G. C. Greubel, Oct 01 2022 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^9 )); // G. C. Greubel, Oct 01 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1+x)*(1-2*x))^9 ).list()
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CROSSREFS
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Ninth (m=8) column of triangle A073370.
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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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