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A174120 Partial sums of A024012. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 01:25 EDT 2020. Contains 336280 sequences. (Running on oeis4.)