OFFSET
0,1
COMMENTS
I used the short MATLAB program from the zip file link altered to produce a Lucas version of the tribonacci numbers.
No term is divisible by 8 or 9. - Vladimir Joseph Stephan Orlovsky, Mar 24 2011
REFERENCES
Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.
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.
T.-X. He, Impulse Response Sequences and Construction of Number Sequence Identities, J. Int. Seq. 16 (2013) #13.8.2
Index entries for linear recurrences with constant coefficients, signature (1,1,1).
FORMULA
a(0)=2; a(1)=1; a(2)=1; a(n) = a(n-1) + a(n-2) + a(n-3).
From R. J. Mathar, Aug 04 2008: (Start)
O.g.f.: (2-x-2*x^2)/(1-x-x^2-x^3). (End)
MATHEMATICA
a[0]=2; a[1]=1; a[2]=1; a[n_]:= a[n]=a[n-1]+a[n-2]+a[n-3]; Table[a[n], {n, 0, 40}] (* Alonso del Arte, Mar 24 2011 *)
LinearRecurrence[{1, 1, 1}, {2, 1, 1}, 40] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
PROG
(Haskell)
a141036 n = a141036_list !! n
a141036_list = 2 : 1 : 1 : zipWith3 (((+) .) . (+))
a141036_list (tail a141036_list) (drop 2 a141036_list)
-- Reinhard Zumkeller, Sep 15 2014
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[2; 1; 1])[1, 1] \\ Charles R Greathouse IV, Jun 15 2015
(PARI) my(x='x+O('x^40)); Vec((2-x-2*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 22 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (2-x-2*x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 22 2019
(Sage) ((2-x-2*x^2)/(1-x-x^2-x^3)).series(x, 41).coefficients(x, sparse=False) # G. C. Greubel, Apr 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Matt Wynne (matwyn(AT)verizon.net), Jul 30 2008
EXTENSIONS
Corrected offset and indices in formulas, R. J. Mathar, Aug 05 2008
Better name from T. D. Noe, Aug 06 2008
STATUS
approved