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A171442
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Expansion of (1+x)^7/(1-x).
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7
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1, 8, 29, 64, 99, 120, 127, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128
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OFFSET
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0,2
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COMMENTS
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a(n)=2^7=128 for n>=7. We observe that this sequence is the transform of A171441 by T such that: T(u_0,u_1,u_2,u_3,u_4,u_5,...)=(u_0,u_0+u_1,u_1+u_2,u_2+u_3,u_3+u_4,...).
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LINKS
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FORMULA
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With m=8, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
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EXAMPLE
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a(5) = C(8,5-0)+C(8,5-2)+C(8,5-4) = 56+56+8 = 120.
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MAPLE
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m:=8:for n from 0 to 40 do a(n):=sum('binomial(m, n-2*k)', k=0..floor(n/2)): od : seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[(1+x)^7/(1-x), {x, 0, 60}], x] (* Harvey P. Dale, Apr 30 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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EXTENSIONS
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STATUS
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approved
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