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A174192
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Expansion of (1-x+2x^2)/ ((1-x)*(1-2x-x^2)).
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1
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1, 2, 7, 18, 45, 110, 267, 646, 1561, 3770, 9103, 21978, 53061, 128102, 309267, 746638, 1802545, 4351730, 10506007, 25363746, 61233501, 147830750, 356895003, 861620758, 2080136521, 5021893802, 12123924127
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n)=2*a(n-1)+a(n-2)+2, with a(0)=1, a(1)=2.
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EXAMPLE
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a(2) = 2*a(1)+a(0)+2 = 2*2+1+2 = 7
a(3) = 2*a(2)+a(1)+2 = 2*7+2+2 = 18.
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MATHEMATICA
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CoefficientList[Series[(1-x+2x^2)/((1-x)*(1-2x-x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, -1, -1}, {1, 2, 7}, 30] (* Harvey P. Dale, Jul 18 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Terms corrected by R. J. Mathar, Oct 26 2011
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STATUS
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approved
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