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8th column of A172119.
4

%I #9 Oct 19 2015 02:41:42

%S 1,2,4,8,16,32,64,128,255,508,1012,2016,4016,8000,15936,31744,63233,

%T 125958,250904,499792,995568,1983136,3950336,7868928,15674623,

%U 31223288,62195672,123891552,246787536,491591936,979233536

%N 8th column of A172119.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,0,0,-1).

%F The generating function is f such that: f(z)=1/(1-2*z+z^8). Recurrence relation: a(n+8)=2*a(n+7)-a(n). General term: a(n) = Sum_{j=0..floor(n/(k+1))} ((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j)) with k=7.

%e a(4) = binomial(4,4)*2^4 = 16.

%e a(9) = binomial(9,9)*2^9 - binomial(2,1)*2^1 = 512 - 4 = 508.

%p k:=7:taylor(1/(1-2*z+z^(k+1)),z=0,30); for k from 0 to 20 do for n from 0 to 30 do b(n):=sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))):od:k: seq(b(n),n=0..30):od;

%Y Cf. A172316, A001949, A107066, A008937, A172119.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, Jan 31 2010