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
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