OFFSET
0,4
LINKS
FORMULA
a(n) = A123344(n+1), n > 0.
a(n) = (-2)^n/4 = (-1)^n*A000079(n-2), n > 1.
O.g.f.: (1 + 3*x + 3*x^2)/(1 + 2*x). - R. J. Mathar, Aug 27 2008
a(n) = -2*a(n-1) for n >= 3; a(0)=1, a(1)=1, a(2)=1. - Harvey P. Dale, May 04 2012
G.f.: x+1/Q(0) where Q(k) = 1 + x*(k+1)/(1 - 1/(1 - (k+1)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Sep 23 2012
G.f.: 1+x/U(0) where U(k) = 1 - x*(k+4) + x*(k+3)/U(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 11 2012
a(n) = A122803(n-2) for n >= 2. - Georg Fischer, Nov 03 2018
E.g.f.: (3/4) + (3/2)*x + (1/4)*exp(-2*x). - Alejandro J. Becerra Jr., Feb 15 2021
MATHEMATICA
CoefficientList[Series[(1+3x+3x^2)/(1+2x), {x, 0, 40}], x] (* or *) Join[ {1, 1}, NestList[-2#&, 1, 38]] (* Harvey P. Dale, May 04 2012 *)
Join[{1, 1}, LinearRecurrence[{-2}, {1}, 32]] (* Ray Chandler, Aug 12 2015 *)
PROG
(PARI) Vec((1 + 3*x + 3*x^2)/(1 + 2*x) + O(x^40)) \\ Andrew Howroyd, Nov 03 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, Aug 12 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Aug 28 2008
STATUS
approved