OFFSET
0,1
COMMENTS
Lexicographically earliest (when ordered) minimal set of generators for A001969 (numbers with an even number of binary 1's) as a group under A003987(.,.) the XOR operation. - Peter Munn, Aug 21 2019
REFERENCES
G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Josef Eschgfäller, Andrea Scarpante, Dichotomic random number generators, arXiv:1603.08500 [math.CO], 2016.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Eric Weisstein's World of Mathematics, Group
Wikipedia, Generating set of a group
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = 2^(n+1)+1.
a(n) = 3*a(n-1) - 2*a(n-2).
O.g.f.: (3-4*x)/(1-3*x+2*x^2). - R. J. Mathar, Nov 23 2007
MATHEMATICA
LinearRecurrence[{3, -2}, {3, 5}, 40] (* Harvey P. Dale, Sep 10 2017 *)
PROG
(Magma) [2^(n+1)+1 : n in [0..40]]; // Vincenzo Librandi, Sep 01 2011
(PARI) x='x+O('x^99); Vec(1/(1-x)+2/(1-2*x)) \\ Altug Alkan, Mar 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved