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A099524
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Expansion of 1/(1-5*x-x^3).
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0
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1, 5, 25, 126, 635, 3200, 16126, 81265, 409525, 2063751, 10400020, 52409625, 264111876, 1330959400, 6707206625, 33800145001, 170331684405, 858365628650, 4325628288251, 21798473125660, 109850731256950, 553579284573001
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OFFSET
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0,2
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COMMENTS
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A transform of A000351 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)).
a(n) equals the number of n-length words on {0,1,2,3,4,5} such that 0 appears only in a run which length is a multiple of 3. - Milan Janjic, Feb 17 2015
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LINKS
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FORMULA
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a(n) = 5*a(n-1) + a(n-3).
a(n) = Sum_(k=0..floor(n/3)) binomial(n-2*k, k)*5^(n-3*k).
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MATHEMATICA
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CoefficientList[Series[1/(1-5x-x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[ {5, 0, 1}, {1, 5, 25}, 30] (* Harvey P. Dale, May 08 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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