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11th column of A172119.
0

%I #6 Feb 21 2016 16:05:03

%S 1,2,4,8,16,32,64,128,256,512,1024,2047,4092,8180,16352,32688,65344,

%T 130624,261120,521984,1043456,2085888,4169729,8335366,16662552,

%U 33308752,66584816,133104288,266077952,531894784,1063267584

%N 11th column of A172119.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,0,0,0,0,0,-1).

%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=10.

%F G.f: f(z)=1/(1-2*z+z^(11)).

%F a(n+11)=2*a(n+10)-a(n).

%e a(12)=C(12,12)*2^12-C(2,1)*2^1=4092.

%p k:=10: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. A172319, A172318, A172317, A172316, A172119, A001949, A107066.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, Jan 31 2010