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A109545
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a(n) = 2*a(n-1) + a(n-2) + a(n-3).
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1
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1, 1, 2, 6, 15, 38, 97, 247, 629, 1602, 4080, 10391, 26464, 67399, 171653, 437169, 1113390, 2835602, 7221763, 18392518, 46842401, 119299083, 303833085, 773807654, 1970747476, 5019135691, 12782826512, 32555536191, 82913034585
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OFFSET
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0,3
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LINKS
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FORMULA
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lim_{n-> infinity} a(n)/a(n-1)= 2.54682...
G.f.: (1-x-x^2)/(1-2*x-x^2-x^3). [Sep 28 2009]
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MATHEMATICA
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a = 2; b = -1; M = {{0, 1, 0, 0, 0}, { a - 2, a - 2, a - 2 - b, a - 2 - b, 0}, {1, 1, 1, 1, 0}, {0, 1, 1, 0, 0}, {0, 0, 0, 1, 1}} v[1] = {1, 1, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] a0 = Table[Abs[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{2, 1, 1}, {1, 1, 2}, 30] (* Harvey P. Dale, Aug 05 2015 *)
Lucas := 1 + x (1 + 2 x)/(1 - x - x^2); (* InvertTransform defined in A052987 *)
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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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Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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STATUS
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approved
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