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 A102002 #23 Feb 26 2020 15:13:11
%S A102002 1,7,13,31,85,199,493,1231,3013,7447,18397,45343,111925,276199,681421,
%T A102002 1681519,4149157,10237879,25262269,62334655,153810709,379529095,
%U A102002 936489133,2310790159,5701884805,14069421655,34716351901,85662734431,211373124853,521564001319
%N A102002 Weighted tribonacci (1,2,4), companion to A102001.
%C A102002 a(n)/a(n-1) tends to 2.46750385...an eigenvalue of M and a root of the characteristic polynomial x^3 - x^2 - 2x - 4. A102001 is generated from [1 1 1 / 2 0 0 / 0 2 0] but has the same characteristic polynomial and recursive multipliers (1,2,4). A101000 uses the recursive multipliers (1,2,4,8).
%H A102002 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,4).
%F A102002 a(n) = a(n-1) + 2*a(n-2) + 4*a(n-3), a>3. a(n) = center term in M^n * [1 1 1], where M = the 3X3 matrix [0 1 0 / 0 0 1 / 4 2 1]; M^n * [1 1 1] = [a(n-1) a(n) a(n+1)].
%F A102002 G.f.: -x*(4*x^2+6*x+1)/(4*x^3+2*x^2+x-1). [_Harvey P. Dale_, Apr 28 2012]
%e A102002 a(6) = 199 = 85 + 2*31 + 4*13 = a(5) + 2*a(4) + 4*a(3).
%e A102002 a(6) = 199 since M^6 * [1 1 1] = [85 199 493] = [a(5) a(6) a(7)].
%t A102002 LinearRecurrence[{1,2,4}, {1,7,13}, 50] (* _Harvey P. Dale_, Apr 28 2012 *)
%o A102002 (Sage)
%o A102002 from sage.combinat.sloane_functions import recur_gen3
%o A102002 it = recur_gen3(1,1,1,1,2,4)
%o A102002 [next(it) for i in range(32)]
%o A102002 # _Zerinvary Lajos_, Jun 25 2008
%Y A102002 Cf. A102000, A102001.
%K A102002 nonn,easy
%O A102002 1,2
%A A102002 _Gary W. Adamson_, Dec 23 2004
%E A102002 More terms from _Harvey P. Dale_, Apr 28 2012