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A144900
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Expansion of x/((1-x-x^3)*(1-x)^6).
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8
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0, 1, 7, 28, 85, 218, 498, 1045, 2055, 3840, 6887, 11945, 20153, 33228, 53741, 85522, 134254, 208344, 320200, 488103, 738951, 1112281, 1666164, 2485845, 3696406, 5481325, 8109676, 11975993, 17658694, 26005706, 38259955, 56243281, 82625979, 121321831, 178067054
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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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G.f.: x/((1-x-x^3)*(1-x)^6).
a(n) = Sum_{j=0..floor((n+5)/3)} binomial(n-2*j+5, j+6).
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MAPLE
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a:= n-> (Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [7, -21, 36, -41, 36, -27, 16, -6, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[x/((1-x-x^3)(1-x)^6), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{7, -21, 36, -41, 36, -27, 16, -6, 1}, {0, 1, 7, 28, 85, 218, 498, 1045, 2055}, 40] (* Harvey P. Dale, Mar 02 2016 *)
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PROG
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(Magma)
A144900:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+5, j+6): j in [0..Floor((n+5)/3)]]) >;
(SageMath)
def A144900(n): return sum(binomial(n-2*j+5, j+6) for j in (0..((n+5)//3)))
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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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