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A329301 a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) - (-1)^n*a(n-2) + 2*a(n-3).

%I A329301 #17 Jul 04 2023 14:11:48
%S A329301 1,1,1,2,3,3,4,7,9,10,15,23,28,35,53,74,91,123,180,239,305,426,599,
%T A329301 783,1036,1451,1981,2602,3523,4883,6564,8727,11929,16330,21855,29383,
%U A329301 40188,54515,73093,98954,134891,182123,245140,332799,451905,609386,823079,1117503,1513196,2041851
%N A329301 a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) - (-1)^n*a(n-2) + 2*a(n-3).
%H A329301 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 2).
%F A329301 G.f.: (-1 - x^2)/(-1 + x - x^2 + 2*x^3). - _Stefano Spezia_, Nov 30 2019
%t A329301 CoefficientList[Series[(-1 - x^2)/(-1 + x - x^2 + 2 x^3), {x, 0, 49}], x] (* _Michael De Vlieger_, Dec 14 2019 *)
%o A329301 (Magma) [1, 1] cat [ n le 3 select n else Self(n-1)-(-1)^n*Self(n-2)+2*Self(n-3): n in [1..55]];
%Y A329301 Cf. A000930.
%K A329301 nonn,easy
%O A329301 0,4
%A A329301 _Juri-Stepan Gerasimov_, Nov 30 2019