A171442 Expansion of (1+x)^7/(1-x).

1, 8, 29, 64, 99, 120, 127, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128

Offset: 0

Author

Richard Choulet, Dec 09 2009

Keywords

• nonn
• easy

Comments

a(n)=2^7=128 for n>=7. We observe that this sequence is the transform of A171441 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(5) = C(8,5-0)+C(8,5-2)+C(8,5-4) = 56+56+8 = 120.
		

Links

• 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, A171443.

Programs

Maple

m:=8: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)^7/(1-x),{x,0,60}],x] (* Harvey P. Dale, Apr 30 2012 *)

Formula

With m=8, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).

Extensions

Definition rewritten by Bruno Berselli, Sep 23 2011