OFFSET
0,1
COMMENTS
A020944(a(n)) = 0. - Reinhard Zumkeller, Mar 13 2011
a(n) + a(n-1)^2 is a perfect square. - Vincenzo Librandi, Oct 28 2011
Number of distinct continued fractions of n terms chosen from {1,2}. - Clark Kimberling, Jul 20 2015
Also, the decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 643", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283508. - Robert Price, Mar 09 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = a(n-1)*2 + 1, a(0)=2.
a(n) = A083329(n+1).
a(n) = A055010(n+1).
G.f.: (2 - x)/((1-x)(1-2x)). - R. J. Mathar, Feb 13 2009
From G. C. Greubel, Sep 01 2016: (Start)
a(n) = 3*a(n-1) - 2*a(n-2).
E.g.f.: 3*exp(2*x) - exp(x). (End)
MATHEMATICA
Table[3*2^n - 1 , {n, 0, 25}] (* G. C. Greubel, Sep 01 2016 *)
LinearRecurrence[{3, -2}, {2, 5}, 40] (* Harvey P. Dale, Mar 01 2024 *)
PROG
(Magma) [3*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011
(PARI) a(n)=3*2^n-1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jan 03 2009
EXTENSIONS
Edited by N. J. A. Sloane, Feb 14 2009
STATUS
approved