Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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