A214899 a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=2, a(1)=1, a(2)=2.

2, 1, 2, 5, 8, 15, 28, 51, 94, 173, 318, 585, 1076, 1979, 3640, 6695, 12314, 22649, 41658, 76621, 140928, 259207, 476756, 876891, 1612854, 2966501, 5456246, 10035601, 18458348, 33950195, 62444144, 114852687, 211247026, 388543857

Offset

0,1

Comments

With offset of 5 this sequence is the 4th row of the tribonacci array A136175.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Robert Price)

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.: (2-x-x^2)/(1-x-x^2-x^3).

a(n) = K(n) - T(n+1) + T(n), where K(n) = A001644(n), T(n) = A000073(n+1). - G. C. Greubel, Apr 23 2019

Mathematica

LinearRecurrence[{1, 1, 1}, {2, 1, 2}, 34] (* Ray Chandler, Dec 08 2013 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[2; 1; 2])[1, 1] \\ Charles R Greathouse IV, Jun 11 2015
(PARI) my(x='x+O('x^40)); Vec((2-x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (2-x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
(Sage) ((2-x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
(GAP) a:=[2, 1, 2];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019

Crossrefs

Cf. A000073, A000213, A035513, A136175, A141036, A141523.

Sequence in context: A052532 A006702 A129394 * A199599 A201163 A049901

Adjacent sequences: A214896 A214897 A214898 * A214900 A214901 A214902

Keyword

nonn,easy

Author

Abel Amene, Jul 29 2012

Status

approved