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%I #24 Jan 03 2024 08:43:48
%S 1,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,
%T 14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,
%U 26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37
%N a(n) = a(n-1) + a(n-2) - a(n-3), for n > 3, with a(0)=1, a(1)=0, a(2)=1, a(3)=1.
%C Diagonal sums of triangle A123110. - _Philippe Deléham_, Oct 08 2009
%H G. C. Greubel, <a href="/A123108/b123108.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F G.f.: (1 -x +x^3)/(1 -x -x^2 +x^3).
%F a(n) = A110654(n-1). - _R. J. Mathar_, Jun 18 2008
%F From _G. C. Greubel_, Jul 21 2021: (Start)
%F a(n) = (1/4)*(2*n - 1 + (-1)^n) + [n=0].
%F E.g.f.: (1/2)*(2 + x*cosh(x) + (x-1)*sinh(x)). (End)
%t LinearRecurrence[{1,1,-1},{1,0,1,1},90] (* _Harvey P. Dale_, Aug 10 2020 *)
%o (Magma) I:=[0,1,1]; [1] cat [n le 3 select I[n] else Self(n-1) +Self(n-2) -Self(n-3): n in [1..31]]; // _G. C. Greubel_, Jul 21 2021
%o (Sage) [(2*n - 1 + (-1)^n)/4 + bool(n==0) for n in (0..90)] # _G. C. Greubel_, Jul 21 2021
%Y Cf. A065033, A110654, A123110.
%K nonn,easy
%O 0,5
%A _Philippe Deléham_, Sep 28 2006
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