A174120 Partial sums of A024012.

1, 2, 2, 1, 1, 8, 36, 115, 307, 738, 1662, 3589, 7541, 15564, 31752, 64295, 129575, 260358, 522178, 1046105, 2094281, 4190992, 8384812, 16772891, 33549531, 67103338, 134211526, 268428525, 536863197, 1073733268, 2147474192

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 08 2010

Keywords

• nonn
• easy

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Programs

Mathematica

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

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

Formula

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