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 A097067 #30 Jul 04 2023 09:52:26 %S A097067 1,0,1,4,12,32,80,192,448,1024,2304,5120,11264,24576,53248,114688, %T A097067 245760,524288,1114112,2359296,4980736,10485760,22020096,46137344, %U A097067 96468992,201326592,419430400,872415232,1811939328,3758096384,7784628224,16106127360,33285996544,68719476736 %N A097067 Expansion of g.f. (1-4*x+5*x^2)/(1-2*x)^2. %C A097067 Binomial transform of A097065. Binomial transform is (n-2)*2^(n-1)+2, or A048495 with an extra leading 1. %H A097067 Vincenzo Librandi, <a href="/A097067/b097067.txt">Table of n, a(n) for n = 0..2000</a> %H A097067 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4). %F A097067 a(n) = (n-1)*2^(n-2) + 5*0^n/4. %F A097067 a(n) = 4*a(n-1) - 4*a(n-2), n > 1. %F A097067 a(n+1) = A001787(n). %F A097067 E.g.f.: (5 - exp(2*x)*(1 - 2*x))/4. - _Stefano Spezia_, Jul 01 2023 %p A097067 a:=n->abs(floor(sum (2^(n-1),j=1..n))): seq(a(n),n=-1..28); # _Zerinvary Lajos_, Jun 27 2007 %o A097067 (Magma) [(n-1)*2^(n-2)+5*0^n/4 : n in [0..30]]; // _Vincenzo Librandi_, Sep 25 2011 %o A097067 (PARI) Vec((1-4*x+5*x^2)/(1-2*x)^2 + O(x^50)) \\ _Altug Alkan_, Nov 13 2015 %Y A097067 Essentially the same as A001787. %Y A097067 Cf. A048495, A097065. %K A097067 nonn,easy %O A097067 0,4 %A A097067 _Paul Barry_, Jul 22 2004