A171418 - OEIS

A171418

Expansion of (1+x)^4/(1-x).

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

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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, ...); 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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Richard Choulet, Une nouvelle formule combinatoire ?, Mathématique et Pédagogie, 157 (2006), p. 53-60.

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

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(5,n-2*k).

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