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%I #6 Feb 29 2016 13:32:42
%S 1,2,4,8,16,32,64,128,256,511,1020,2036,4064,8112,16192,32320,64512,
%T 128768,257025,513030,1024024,2043984,4079856,8143520,16254720,
%U 32444928,64761088,129265151,258017272,515010520,1027977056
%N 9th column of the array A172119.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,0,0,0,-1).
%F G.f.: f such that: f(z)=1/(1-2*z+z^9).
%F a(n) = sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))) with k=8.
%F Recurrence relation: a(n+9) = 2*a(8) - a(n).
%e a(7)=C(7,7)*2^7=128. a(10)=C(10,10)*2^10-C(2,1)*2^1=1020.
%p 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; k:=8:taylor(1/(1-2*z+z^(k+1)),z=0,30);
%Y Cf. A172317, A172316, A172119, A001949, A107066.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Jan 31 2010
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