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%I #11 Oct 01 2023 20:15:39
%S -1,2,1,0,4,4,5,12,17,26,46,72,115,190,305,492,800,1292,2089,3384,
%T 5473,8854,14330,23184,37511,60698,98209,158904,257116,416020,673133,
%U 1089156,1762289,2851442,4613734,7465176,12078907,19544086,31622993,51167076
%N Expansion of (-1+2x+2x^2)/((1+x+x^2)(1-x-x^2)).
%C This sequence was investigated in cooperation with Paul Barry. Generating floretion: - 0.5'i - 0.5'k - 0.5j' - 0.5'ii' + 0.5'jj' - 0.5'kk' + 0.5'ik' - 0.5'ki' ("les").
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 2, 1).
%F a(n) = Fib(n+1)/2 - sqrt(3)cos(2Pi*n/3 + Pi/6); a(n) = a(n-2) + 2a(n-3) + a(n-4), a(0) = -1, a(1) = 2, a(2) = 1, a(3) = 0
%t a[n_] := Fibonacci[n + 1]/2 - Sqrt[3]Cos[2Pi*n/3 + Pi/6]; Table[ a[n], {n, 0, 39}]
%t a[0] = -1; a[1] = 2; a[2] = 1; a[3] = 0; a[n_] := a[n] = a[n - 2] + 2a[n - 3] + a[n - 4]; Table[ a[n], {n, 0, 39}]
%t CoefficientList[ Series[(-1 + 2x + 2x^2)/((1 - x - x^2)(1 + x + x^2)), {x, 0, 39}], x] (* _Robert G. Wilson v_, Dec 02 2004 *)
%o (PARI) Vec((-1+2*x+2*x^2)/((1+x+x^2)*(1-x-x^2))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A100886, A100888, A100889, A100890.
%K sign,easy
%O 0,2
%A _Creighton Dement_, Nov 21 2004
%E Edited and extended by _Robert G. Wilson v_, Dec 02 2004
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