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 A119916 #11 Feb 18 2016 10:40:00
%S A119916 0,1,4,17,64,233,820,2825,9568,31985,105796,346913,1129312,3653657,
%T A119916 11758132,37665881,120172096,382039649,1210689028,3825777329,
%U A119916 12058462720,37918780361,118986517684,372650082857,1165021837984
%N A119916 Number of runs of 0's of odd length in all ternary words of length n.
%C A119916 a(n)=Sum(k*A119914(n,k),k>=0).
%C A119916 Binomial transform of A179608. - _Johannes W. Meijer_, Aug 01 2010
%H A119916 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3,-9).
%F A119916 G.f. = z(1-z)/[(1+z)(1-3z)^2].
%F A119916 a(n) = ((-1)^(n-1)+(3+4*n)*3^(n-1))/8. - _Johannes W. Meijer_, Aug 01 2010
%e A119916 a(2)=4 because in the nine ternary words of length 2, namely, 00, (0)1, (0)2, 1(0), 11, 12, 2(0), 21, 22, we have altogether 4 runs of 0's of odd length (shown between parentheses).
%p A119916 g:=z*(1-z)/(1-3*z)^2/(1+z): gser:=series(g,z=0,35): seq(coeff(gser,z,n),n=0..28);
%t A119916 LinearRecurrence[{5,-3,-9},{0,1,4},30] (* _Harvey P. Dale_, Feb 18 2016 *)
%Y A119916 Cf. A119914.
%K A119916 nonn,easy
%O A119916 0,3
%A A119916 _Emeric Deutsch_, May 29 2006