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A171443
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Expansion of (1+x)^8/(1-x).
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9
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1, 9, 37, 93, 163, 219, 247, 255, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256
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OFFSET
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0,2
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COMMENTS
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a(n)=2^8=256 for n>=8. We observe that this sequence is the transform of A171442 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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REFERENCES
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Richard Choulet, Une nouvelle formule de combinatoire, Mathématique et Pédagogie, 157 (2006), p. 53-60.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1).
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FORMULA
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With m=9, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
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EXAMPLE
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a(7) = C(9,7-0)+C(9,7-2)+C(9,7-4)+C(9,7-6) = 36+126+84+9 = 255.
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MAPLE
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m:=9: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)^8/(1-x), {x, 0, 80}], x] (* Harvey P. Dale, Jul 22 2014 *)
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CROSSREFS
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Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171442.
Sequence in context: A200774 A273220 A022276 * A341403 A320696 A299290
Adjacent sequences: A171440 A171441 A171442 * A171444 A171445 A171446
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KEYWORD
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nonn,easy
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AUTHOR
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Richard Choulet, Dec 09 2009
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EXTENSIONS
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Definition rewritten by Bruno Berselli, Sep 23 2011
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STATUS
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approved
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