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A226308
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a(n) = a(n-1) + a(n-2) + 2*a(n-3) with a(0)=2, a(1)=1, a(2)=5.
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5
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2, 1, 5, 10, 17, 37, 74, 145, 293, 586, 1169, 2341, 4682, 9361, 18725, 37450, 74897, 149797, 299594, 599185, 1198373, 2396746, 4793489, 9586981, 19173962, 38347921, 76695845, 153391690, 306783377, 613566757, 1227133514, 2454267025, 4908534053, 9817068106, 19634136209
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: -(2*x^2-x+2) / ((2*x-1)*(x^2 + x + 1)). - Colin Barker, Jun 08 2013
E.g.f.: (1/7)*(8*exp(2*x) + exp(-x/2)*(6*cos(sqrt(3)*x/2) - 4*sqrt(3)*sin(sqrt(3)*x/2))) (Charles K. Cook and Michael R. Bacon, 2013).
a(n) = (1/7)*(2^(n+3) + 6*cos(2*Pi*n/3) - 4*sqrt(3)*sin(2*Pi*n/3)). (End)
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MAPLE
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A226308 := n -> 1/7*(2^(n+3) + 6*cos(2*Pi*n/3) - 4*sqrt(3)*sin(2*Pi*n/3)):
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MATHEMATICA
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CoefficientList[Series[-(2 x^2 - x + 2) / ((2 x - 1) (x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 18 2013 *)
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PROG
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(Python)
a0, a1, a2 = 2, 1, 5
for n in range(77):
a = a2 + a1 + 2*a0
print a0,
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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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Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021
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STATUS
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approved
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