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 A134396 #28 Mar 13 2024 16:03:02
%S A134396 1,3,9,27,80,232,656,1808,4864,12800,33024,83712,208896,514048,
%T A134396 1249280,3002368,7143424,16842752,39387136,91422720,210763776,
%U A134396 482869248,1099956224,2492465152,5620367360,12616466432,28202500096,62797119488,139318001664,308029685760
%N A134396 A007318 * A000125.
%C A134396 a(n) is the number of ternary strings of length n that contain at most three 0's.- _Enrique Navarrete_, Mar 13 2024
%H A134396 Colin Barker, <a href="/A134396/b134396.txt">Table of n, a(n) for n = 0..1000</a>
%H A134396 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F A134396 Binomial transform of A000125. Row sums of triangle A134395.
%F A134396 O.g.f.: (1-x)*(1-4*x+5*x^2) / (1-2*x)^4. - _R. J. Mathar_, Jun 08 2008
%F A134396 From _Colin Barker_, Feb 13 2017: (Start)
%F A134396 a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>3.
%F A134396 a(n) = (2^(n-4)*(48 + 20*n + 3*n^2 + n^3)) / 3. (End)
%F A134396 E.g.f.: e^(2*x)*(1+x+x^2/2+x^3/6). - _Enrique Navarrete_, Mar 13 2024
%e A134396 a(3) = 27 = (1, 3, 3, 1) dot (1, 2, 4, 8) = (1 + 6 + 12 + 8), where A000125 = (1, 2, 4, 8, 15, 26, 42, ...).
%e A134396 a(3) = 27 = sum of row 3 terms of triangle A134395: (8 + 12 + 6 + 1).
%t A134396 CoefficientList[Series[(1-x)(1-4x+5x^2)/(1-2x)^4,{x,0,30}],x] (* or *) LinearRecurrence[ {8,-24,32,-16},{1,3,9,27},30] (* _Harvey P. Dale_, Mar 09 2023 *)
%o A134396 (PARI) Vec((1-x)*(1-4*x+5*x^2) / (1-2*x)^4 + O(x^30)) \\ _Colin Barker_, Feb 13 2017
%Y A134396 Cf. A134395, A000125.
%K A134396 nonn,easy
%O A134396 0,2
%A A134396 _Gary W. Adamson_, Oct 23 2007
%E A134396 More terms from _R. J. Mathar_, Jun 08 2008