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%I #10 Jul 30 2015 01:28:58
%S 3,1,2,7,7,12,23,33,54,91,143,232,379,609,986,1599,2583,4180,6767,
%T 10945,17710,28659,46367,75024,121395,196417,317810,514231,832039,
%U 1346268,2178311,3524577,5702886,9227467,14930351,24157816,39088171,63245985
%N Expansion of (3+x-x^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' ("jes"). A100885(n) = (1/2)(A100886(n) + A100887(n) - a(n)).
%F a(n) = Fib(n+2) + sqrt(3)cos(2Pi*n/3 + Pi/6) + sin(2Pi*n/3 + Pi/6); a(n) = a(n-2) + 2a(n-3) + a(n-4), a(0) = 3, a(1) = 1, a(2) = 2, a(3) = 7.
%t a[0] = 3; a[1] = 1; a[2] = 2; a[3] = 7; a[n_] := a[n] = a[n - 2] + 2a[n - 3] + a[n - 4]; Table[ a[n], {n, 0, 37}] (* _Robert G. Wilson v_, Nov 26 2004 *)
%t CoefficientList[ Series[(3 + x - x^2)/((1 + x + x^2)(1 - x - x^2)), {x, 0, 37}], x] (* _Robert G. Wilson v_, Nov 26 2004 *)
%o (PARI) Vec((3+x-x^2)/((1+x+x^2)*(1-x-x^2))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A100885, A100886, A100887, A100889, A100890.
%K nonn,easy
%O 0,1
%A _Creighton Dement_, Nov 21 2004
%E More terms from _Robert G. Wilson v_, Nov 26 2004
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