OFFSET
0,2
COMMENTS
Tribonacci sequence beginning 0, 2, 1.
Pisano period lengths: 1, 4, 13, 8, 31, 52, 48, 16, 39, 124, 110, 104, 168, 48, 403, 32, 96, 156, 360, 248,.... - R. J. Mathar, Aug 10 2012
One bisection is 0, 1, 6, 19, 64, 217, 734, 2483, 8400,.. and the other 2, 3, 10, 35, 118, 399, 1350, 4567,... both with recurrence b(n)=3*b(n-1)+b(n-2)+b(n-3). - R. J. Mathar, Aug 10 2012
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).
FORMULA
G.f.: x*(2-x)/(1-x-x^2-x^3).
a(n) = 2*a(n-1) - a(n-4), n>3. - Vincenzo Librandi, Jun 08 2011
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {0, 2, 1}, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 07 2011 *)
PROG
(PARI) x='x+O('x^30); concat([0], Vec(x*(2-x)/(1-x-x^2-x^3))) \\ G. C. Greubel, Feb 09 2018
(Magma) I:=[0, 2, 1]; [n le 3 select I[n] else Self(n-1) + Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 09 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved