OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-3).
FORMULA
a(n) = (-1)^n*A133494(n-1), n>0.
G.f.: (-x)*(1 + 2*x)/(1+3*x). - R. J. Mathar, Nov 11 2008
G.f.: x^2/( Q(0)+ 2*x)- x where Q(k) = 1 - x/(x*(k+1) - 1 )/Q(k+1) ; (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 24 2013
E.g.f.: (exp(-3*x) - (1 + 6*x))/9. - Wolfdieter Lang, Apr 19 2017
a(n) = (-3)^(n-2) for n >= 2, with a(0) = 0 and a(1) = -1. - G. C. Greubel, Mar 30 2021
MAPLE
MATHEMATICA
CoefficientList[Series[-x(1+2x)/(1+3x), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 24 2013 *)
Join[{0, -1}, LinearRecurrence[{-3}, {1}, 26]] (* Ray Chandler, Aug 12 2015 *)
PROG
(Magma) [0, -1] cat [(-3)^(n-2): n in [2..30]]; // G. C. Greubel, Mar 30 2021
(Sage) [-n if n<2 else (-3)^(n-2) for n in (0..30)] # G. C. Greubel, Mar 30 2021
CROSSREFS
Cf. A285066 (alternating row sums, starting here with n >= 2). - Wolfdieter Lang, Apr 23 2017
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Aug 04 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Nov 11 2008
STATUS
approved