This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A077946 #14 Jun 04 2021 23:23:40 %S A077946 1,1,3,7,15,35,79,179,407,923,2095,4755,10791,24491,55583,126147, %T A077946 286295,649755,1474639,3346739,7595527,17238283,39122815,88790435, %U A077946 201512631,457339131,1037945263,2355648787,5346217575,12133405675,27537138399,62496384899,141837473047 %N A077946 Expansion of 1/(1 - x - 2*x^2 - 2*x^3). %C A077946 Discarding the first 1 = INVERT transform of [1,2,2,0,0,0,...]. - _Gary W. Adamson_, Feb 16 2010 %H A077946 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,2). %F A077946 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 A077946 (PARI) Vec(1/(1-x-2*x^2-2*x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012 %Y A077946 Cf. A077970. %K A077946 nonn,easy %O A077946 0,3 %A A077946 _N. J. A. Sloane_, Nov 17 2002