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A171442 Expansion of (1+x)^7/(1-x). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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,...).
LINKS
Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
FORMULA
With m=8, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
EXAMPLE
a(5) = C(8,5-0)+C(8,5-2)+C(8,5-4) = 56+56+8 = 120.
MAPLE
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);
MATHEMATICA
CoefficientList[Series[(1+x)^7/(1-x), {x, 0, 60}], x] (* Harvey P. Dale, Apr 30 2012 *)
CROSSREFS
Sequence in context: A299802 A299678 A300310 * A341402 A247541 A320695
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Dec 09 2009
EXTENSIONS
Definition rewritten by Bruno Berselli, Sep 23 2011
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)