A171442 - OEIS

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

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OFFSET

0,2

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,...).

LINKS

Table of n, a(n) for n=0..52.

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).

FORMULA

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

EXAMPLE

a(5) = C(8,5-0)+C(8,5-2)+C(8,5-4) = 56+56+8 = 120.

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 *)