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%I #14 Jun 04 2021 23:23:40
%S 1,1,3,7,15,35,79,179,407,923,2095,4755,10791,24491,55583,126147,
%T 286295,649755,1474639,3346739,7595527,17238283,39122815,88790435,
%U 201512631,457339131,1037945263,2355648787,5346217575,12133405675,27537138399,62496384899,141837473047
%N Expansion of 1/(1 - x - 2*x^2 - 2*x^3).
%C Discarding the first 1 = INVERT transform of [1,2,2,0,0,0,...]. - _Gary W. Adamson_, Feb 16 2010
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,2).
%F a(n) = leftmost term in M^n * [1 0 0], where M = the 3X3 matrix [1 1 1 / 2 0 0 / 0 1 0]. a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3). a(n)/a(n-1) tends to 2.26953084..., an eigenvalue of M and a root of the characteristic polynomial x^3 - x^2 - 2x - 2. a(6) = 79 = 35 + 2*15 + 2*7 = a(5) + 2*a(4) + 2*a(3). - _Gary W. Adamson_, Dec 21 2004
%o (PARI) Vec(1/(1-x-2*x^2-2*x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A077970.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002
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