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
Robert Price, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).
FORMULA
G.f.: (1+8*x-x^2)/(1-x-x^2-x^3).
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {1, 9, 9}, 40] (* Harvey P. Dale, Oct 11 2017 *)
PROG
(PARI) Vec((x^2-8*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jul 08 2014
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+8*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019
(SageMath) ((1+8*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019
(GAP) a:=[1, 9, 9];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Abel Amene, Aug 07 2012
STATUS
approved