OFFSET
0,2
COMMENTS
Part of a group of sequences defined by a(0), a(1)=a(2), a(n) = a(n-1) + a(n-2) + a(n-3) which is a subgroup of sequences with linear recurrences and constant coefficients listed in the index. See Comments in A214727.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..3770
Martin Burtscher, Igor Szczyrba, and RafaĆ 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.: (1+2*x-x^2)/(1-x-x^2-x^3).
a(n) = K(n) - 2*T(n+1) + 4*T(n), where K(n) = A001644(n), and T(n) = A000073(n+1). - G. C. Greubel, Apr 23 2019
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {1, 3, 3}, 40] (* Harvey P. Dale, Oct 05 2013 *)
PROG
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[1; 3; 3])[1, 1] \\ Charles R Greathouse IV, Mar 22 2016
(PARI) my(x='x+O('x^40)); Vec((1+2*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+2*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
(SageMath) ((1+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:=[1, 3, 3];; 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
KEYWORD
nonn,easy
AUTHOR
Abel Amene, Jul 28 2012
STATUS
approved