A168298 a(n) = 1 - n^2*2^n.

1, -1, -15, -71, -255, -799, -2303, -6271, -16383, -41471, -102399, -247807, -589823, -1384447, -3211263, -7372799, -16777215, -37879807, -84934655, -189267967, -419430399, -924844031, -2030043135, -4437573631, -9663676415, -20971519999, -45365592063

Offset

0,3

Comments

Numerator of 2^(-n) - n^2.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

Formula

a(n)= 7*a(n-1) -18*a(n-2) +20*a(n-3) -8*a(n-4) = 1-A007758(n). - R. J. Mathar, Nov 24 2009

G.f.: -(4*x^3-10*x^2+8*x-1) / ((x-1)*(2*x-1)^3). - Colin Barker, Feb 10 2015

E.g.f.: exp(x) - 2*x*(1 + 2*x)*exp(2*x). - G. C. Greubel, Jul 17 2016

Mathematica

f[n_]:=2^n-n^2; Table[Numerator[f[n]], {n, 0, -50, -1}]
LinearRecurrence[{7, -18, 20, -8}, {1, -1, -15, -71}, 30] (* Harvey P. Dale, May 14 2019 *)

Prog

(PARI) Vec(-(4*x^3-10*x^2+8*x-1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Feb 10 2015
(Magma) [1-n^2*2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2016

Crossrefs

Cf. A024012

Sequence in context: A253476 A308596 A145053 * A126274 A241234 A212097

Adjacent sequences: A168295 A168296 A168297 * A168299 A168300 A168301

Keyword

sign,easy

Author

Vladimir Joseph Stephan Orlovsky, Nov 22 2009

Extensions

Offset corrected, keyword:sign added, and definition simplified by R. J. Mathar, Nov 23 2009

Status

approved