A171443 Expansion of g.f. (1+x)^8/(1-x).

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

Offset: 0

Author

Richard Choulet, Dec 09 2009

Keywords

• nonn
• easy

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,...).

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

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

Programs

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 *)

Formula

With m=9, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).

Extensions

Definition rewritten by Bruno Berselli, Sep 23 2011