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Partial sums of A024012.
1

%I #6 Jun 13 2015 00:53:29

%S 1,2,2,1,1,8,36,115,307,738,1662,3589,7541,15564,31752,64295,129575,

%T 260358,522178,1046105,2094281,4190992,8384812,16772891,33549531,

%U 67103338,134211526,268428525,536863197,1073733268,2147474192

%N Partial sums of A024012.

%C A024012 2^n-n^2 -> 1,1,0,-1,0,7,28,79,192,431,924,1927,3952,..

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).

%F a(n) = (-1+2^n-n/6+n^2/2-n^3/3). G.f.: -x*(x^3+4*x^2-4*x+1) / ((x-1)^4*(2*x-1)). - _Colin Barker_, Oct 27 2014

%t f[n_]:=Sum[2^i-i^2,{i,0,n}];Table[f[n],{n,0,5!}]

%o (PARI) Vec(-x*(x^3+4*x^2-4*x+1)/((x-1)^4*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Oct 27 2014

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Mar 08 2010