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A171443 Expansion of (1+x)^8/(1-x). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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,...).

REFERENCES

Richard Choulet, Une nouvelle formule de combinatoire, Mathematique et Pedagogie, 157 (2006), p. 53-60.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

With m=9, a(n)=sum(C(m,n-2*k),k=0..floor(n/2)).

EXAMPLE

a(7) = C(9,7-0)+C(9,7-2)+C(9,7-4)+C(9,7-6) = 36+126+84+9 = 255.

MAPLE

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);

MATHEMATICA

CoefficientList[Series[(1+x)^8/(1-x), {x, 0, 80}], x] (* Harvey P. Dale, Jul 22 2014 *)

CROSSREFS

Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171442.

Sequence in context: A200774 A273220 A022276 * A320696 A299290 A304290

Adjacent sequences:  A171440 A171441 A171442 * A171444 A171445 A171446

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 October 21 23:02 EDT 2018. Contains 316431 sequences. (Running on oeis4.)