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 A172318 #9 Mar 28 2025 10:45:48 %S A172318 1,2,4,8,16,32,64,128,256,511,1020,2036,4064,8112,16192,32320,64512, %T A172318 128768,257025,513030,1024024,2043984,4079856,8143520,16254720, %U A172318 32444928,64761088,129265151,258017272,515010520,1027977056 %N A172318 9th column of the array A172119. %H A172318 <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 A172318 G.f.: 1/(1-2*z+z^9). %F A172318 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 A172318 Recurrence relation: a(n+9) = 2*a(8) - a(n). %e A172318 a(7)=C(7,7)*2^7=128. a(10)=C(10,10)*2^10-C(2,1)*2^1=1020. %p A172318 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 A172318 Cf. A172317, A172316, A172119, A001949, A107066. %Y A172318 Partial sums of A079262. %K A172318 easy,nonn %O A172318 0,2 %A A172318 _Richard Choulet_, Jan 31 2010