OFFSET
0,1
COMMENTS
Inverse binomial transform of A048573.
This is an example of the case k=-1 of sequences with recurrences a(n) = k*a(n-1) + (k+3)*a(n-2) - (2*k+2)*a(n-3).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,2).
FORMULA
a(n) = -a(n-1) + 2*a(n-2).
G.f.: (2+3*x)/((1-x)*(1+2*x)).
a(n+1) - a(n) = (-1)^(n+1)*A000079(n).
a(n+3) = (-1)^n*A083582(n).
a(n+1) - 2*a(n) = -a(n+2).
E.g.f.: (5*exp(x) + exp(-2*x))/3. - Stefano Spezia, Jul 27 2024
MATHEMATICA
(5+(-2)^Range[0, 30])/3 (* or *) LinearRecurrence[{-1, 2}, {2, 1}, 40] (* Harvey P. Dale, Apr 23 2019 *)
PROG
(Magma) [( 5+(-2)^n)/3: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
(PARI) a(n)=(5+(-2)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Cf. A048573.
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Jul 27 2008
EXTENSIONS
Definition simplified by R. J. Mathar, Sep 11 2009
STATUS
approved