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%I #25 Dec 14 2023 05:16:03
%S 0,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,
%T 1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
%U 2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2
%N G.f.: x*(1+x)^2/(1-x^3).
%C Period 3. Used in A042965.
%C First differences are essentially A049347. The binomial transform yields 0, 1, 4, 10,... i.e. A111927 with the first two zeros removed. - _R. J. Mathar_, May 14 2008
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F a(n) = A100063(n+1), n>0. - _R. J. Mathar_, Sep 01 2008
%t LinearRecurrence[{0,0,1},{0,1,2,1},120] (* _Harvey P. Dale_, Aug 01 2016 *)
%o (PARI) x='x+O('x^50); Vec(x*(1+x)^2/(1-x^3)) \\ _G. C. Greubel_, May 03 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 17 2007
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