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

1,2

Comments

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

Links

Table of n, a(n) for n=1..31.

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

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A011296 A176602 A322194 * A240939 A016739 A158452

Adjacent sequences: A174117 A174118 A174119 * A174121 A174122 A174123

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 08 2010

Status

approved