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 A120926 #14 Jun 29 2023 19:09:29
%S A120926 1,4,16,60,216,756,2592,8748,29160,96228,314928,1023516,3306744,
%T A120926 10628820,34012224,108413964,344373768,1090516932,3443737680,
%U A120926 10847773692,34093003032,106928054964,334731302496,1046035320300,3263630199336,10167463313316,31632108085872
%N A120926 Number of isolated 0's in all ternary words of length n on {0,1,2}.
%C A120926 This is essentially the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - 2 S); see A291000. - _Clark Kimberling_, Aug 24 2017
%H A120926 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -9).
%F A120926 a(n) = (4/27)*(n+1)*3^n for n >= 2.
%F A120926 G.f.: z*(1-z)^2/(1-3*z)^2.
%F A120926 a(n) = Sum_{k=0..ceiling(n/2)} k*A120924(n,k).
%e A120926 a(2) = 4 because in the 9 ternary words of length 2, namely 00, 01, 02, 10, 11, 12, 20, 21 and 22, we have altogether 4 isolated 0's.
%p A120926 1,seq(4*(n+1)*3^n/27,n=2..28);
%Y A120926 Cf. A120924.
%K A120926 nonn
%O A120926 1,2
%A A120926 _Emeric Deutsch_, Jul 16 2006