A171443 - OEIS

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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

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OFFSET

0,2

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,...).

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).

FORMULA

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

EXAMPLE

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

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 *)