|
%I #13 Jan 28 2021 16:43:46
%S 0,0,0,1,4,16,60,212,728,2444,8064,26256,84576,270048,855936,2696080,
%T 8446912,26341696,81812544,253181888,781005440,2402311616,7370247168,
%U 22558917120,68901651456,210037106688,639127277568,1941624275200,5889576530944,17839902853120
%N Number of ternary words of length n with exactly one 000.
%C Except for the initial three zeros, convolution of A077835 with itself. Column 1 of A119825.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-4,-12,-8,-4).
%F G.f.: z^3/(1-2z-2z^2-2z^3)^2.
%e a(4)=4 because we have 0001, 0002, 1000 and 2000.
%p h:=z^3/(1-2*z-2*z^2-2*z^3)^2: hser:=series(h,z=0,33): seq(coeff(hser,z,n), n=0..30);
%t LinearRecurrence[{4,0,-4,-12,-8,-4},{0,0,0,1,4,16},40] (* _Harvey P. Dale_, Jan 28 2021 *)
%Y Cf. A077835, A119825, A119826 (without 000), A231430 (one or more 000).
%K nonn,easy
%O 0,5
%A _Emeric Deutsch_, May 26 2006
|
