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A171418 Expansion of (1+x)^4/(1-x). 10
1, 5, 11, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n>=4 a(n)=2^4=16. This sequence is the transform of A115291 by the following transform T: T(u_0,u_1,u_2,u_3,u_4,...)=(u_0,u_0+u_1, u_1+u_2,u_2+u_3,aso); we observe that T(A040000)=A113311 and also T(A113311)=A115291...

Also continued fraction expansion of (55305+sqrt(65))/46231. - Bruno Berselli, Sep 23 2011

REFERENCES

(Revue) 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..200

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

FORMULA

a(n) = sum(C(5,n-2*k),k=0..floor(n/2)).

EXAMPLE

a(3)=C(5,3-0)+C(5,3-2)=10+5=15.

MAPLE

m:=5:for n from 0 to m+1 do a(n):=sum('binomial(m, n-2*k)', k=0..floor(n/2)): od : seq(a(n), n=0..m+1);

CROSSREFS

Cf. A040000, A113311, A115291, A171440, A171441, A171442, A171443.

Sequence in context: A137002 A091718 A078002 * A213444 A137004 A137005

Adjacent sequences:  A171415 A171416 A171417 * A171419 A171420 A171421

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Dec 08 2009

EXTENSIONS

Definition rewritten by Bruno Berselli, Sep 23 2011

STATUS

approved

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Last modified February 18 02:20 EST 2018. Contains 299297 sequences. (Running on oeis4.)