This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A172319 #11 Mar 28 2025 11:01:07
%S A172319 1,2,4,8,16,32,64,128,256,512,1023,2044,4084,8160,16304,32576,65088,
%T A172319 130048,259840,519168,1037313,2072582,4141080,8274000,16531696,
%U A172319 33030816,65996544,131863040,263466240,526413312,1051789311
%N A172319 10th column of A172119.
%H A172319 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,0,0,0,0,-1).
%F A172319 G.f.: 1/(1-2*z+z^10).
%F A172319 a(n)=sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))). a(n+10)=2*a(n+9)-a(n).
%p A172319 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;
%t A172319 LinearRecurrence[{2,0,0,0,0,0,0,0,0,-1},{1,2,4,8,16,32,64,128,256,512},40] (* _Harvey P. Dale_, Sep 22 2020 *)
%Y A172319 Cf. A172318, A172317, A172316, A172119, A001949, A107066.
%Y A172319 Partial sums of A104144.
%K A172319 easy,nonn
%O A172319 0,2
%A A172319 _Richard Choulet_, Jan 31 2010