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A144902
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Expansion of x/((1-x-x^3)*(1-x)^8).
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8
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0, 1, 9, 45, 166, 505, 1342, 3224, 7161, 14938, 29602, 56211, 102973, 182963, 316694, 535947, 889454, 1451305, 2333356, 3703510, 5812615, 9034001, 13921551, 21294946, 32364747, 48915873, 73576675, 110213470, 164508959, 244810154, 363371304, 538175735
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (9,-36,85,-134,154,-140,106,-65,29,-8,1).
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FORMULA
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G.f.: x/((1-x-x^3)*(1-x)^8).
a(n) = Sum_{j=0..floor((n+7)/3)} binomial(n-2*j+7, j+8).
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MAPLE
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a:= n-> (Matrix(11, (i, j)-> if i=j-1 then 1 elif j=1 then [9, -36, 85, -134, 154, -140, 106, -65, 29, -8, 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)^8), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
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PROG
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(Magma)
A144903:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+7, j+8): j in [0..Floor((n+7)/3)]]) >;
(SageMath)
def A144903(n): return sum(binomial(n-2*j+7, j+8) for j in (0..((n+7)//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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