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

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

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

Sequence in context: A137002 A091718 A078002 * A213444 A314002 A137004

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