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 A145070 #16 Aug 22 2020 18:52:53
%S A145070 3,9,20,40,77,147,282,546,1067,2101,4160,8268,16473,32871,65654,
%T A145070 131206,262295,524457,1048764,2097360,4194533,8388859,16777490,
%U A145070 33554730,67109187,134218077,268435832,536871316,1073742257,2147484111
%N A145070 Partial sums of A006127, starting at n=1.
%H A145070 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A145070 a(1) = 3; a(n) = a(n-1) + 2^n + n for n > 1.
%F A145070 From _Colin Barker_, Oct 27 2014: (Start)
%F A145070 a(n) = (-4+2^(2+n)+n+n^2)/2.
%F A145070 a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4).
%F A145070 G.f.: x*(2*x^2-6*x+3) / ((x-1)^3*(2*x-1)).
%F A145070 (End)
%e A145070 a(2) = a(1) + 2^2 + 2 = 3 + 4 + 2 = 9; a(3) = a(2) + 2^3 + 3 = 9 + 8 + 3 = 20.
%p A145070 A145070:=n->(-4+2^(2+n)+n+n^2)/2: seq(A145070(n), n=1..50); # _Wesley Ivan Hurt_, Jan 22 2017
%t A145070 lst={};s=0;Do[s+=2^n+n;AppendTo[lst,s],{n,5!}];lst
%t A145070 Accumulate[Table[2^n+n,{n,50}]] (* or *) LinearRecurrence[{5,-9,7,-2},{3,9,20,40},50] (* _Harvey P. Dale_, Aug 22 2020 *)
%o A145070 (ARIBAS) a:=0; for n:=1 to 30 do a:=a+2**n+n; write(a, ","); end;
%o A145070 (PARI) Vec(x*(2*x^2-6*x+3) / ((x-1)^3*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Oct 27 2014
%Y A145070 Cf. A006127 (2^n + n), A000325 (2^n - n), A048492 (partial sums of A000325, starting at n=1).
%K A145070 nonn,easy
%O A145070 1,1
%A A145070 _Vladimir Joseph Stephan Orlovsky_, Sep 30 2008
%E A145070 Edited by _Klaus Brockhaus_, Oct 14 2008