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A159288 Expansion of (1 + x + x^2)/(1 - x^2 - 2*x^3).

%I A159288 #29 Mar 23 2023 06:16:09
%S A159288 1,1,2,3,4,7,10,15,24,35,54,83,124,191,290,439,672,1019,1550,2363,
%T A159288 3588,5463,8314,12639,19240,29267,44518,67747,103052,156783,238546,
%U A159288 362887,552112,839979,1277886,1944203,2957844,4499975,6846250,10415663
%N A159288 Expansion of (1 + x + x^2)/(1 - x^2 - 2*x^3).
%C A159288 A floretion-generated sequence: 'i + 0.5('ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj')
%C A159288 Starting with offset 1 the sequence appears to be the INVERT transform of (1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, ...). - _Gary W. Adamson_, Aug 27 2016
%H A159288 G. C. Greubel, <a href="/A159288/b159288.txt">Table of n, a(n) for n = 0..1000</a>
%H A159288 Creighton Dement, <a href="http://fumba.eu/sitelayout/Floretion.php">Online Floretion Multiplier</a> [broken link]
%H A159288 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2).
%F A159288 a(n) = A159287(n) + A159287(n+1) + A159287(n+2). - _R. J. Mathar_, Apr 10 2009
%F A159288 a(n) = a(n-2) + 2*a(n-3) for n>2. - _Colin Barker_, Apr 29 2019
%F A159288 a(n)= A052947(n) + A052947(n-1) +A052947(n-2). - _R. J. Mathar_, Mar 23 2023
%t A159288 CoefficientList[Series[(1+x+x^2)/(1-x^2-2x^3),{x,0,50}],x]  (* _Harvey P. Dale_, Mar 09 2011 *)
%t A159288 LinearRecurrence[{0, 1, 2}, {1, 1, 2}, 50] (* _G. C. Greubel_, Jun 27 2018 *)
%o A159288 (PARI) a(n)=([0,1,0; 0,0,1; 2,1,0]^n*[1;1;2])[1,1] \\ _Charles R Greathouse IV_, Aug 27 2016
%o A159288 (PARI) Vec((1 + x + x^2) / (1 - x^2 - 2*x^3) + O(x^40)) \\ _Colin Barker_, Apr 29 2019
%o A159288 (Magma) I:=[1, 1, 2]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jun 27 2018
%Y A159288 Cf. A159284, A159285, A159286, A159287.
%K A159288 easy,nonn
%O A159288 0,3
%A A159288 _Creighton Dement_, Apr 08 2009