%I A143454
%S A143454 1,4,7,10,13,25,46,76,115,190,328,556,901,1471,2455,4123,6826,11239,
%T A143454 18604,30973,51451,85168,140980,233899,388252,643756,1066696,1768393,
%U A143454 2933149,4864417,8064505,13369684,22169131,36762382,60955897,101064949
%N A143454 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=3.
%C A143454 a(n) is also the number of length n quaternary words with at least 3 
               0-digits between any other digits.
%F A143454 G.f.: 1/(x^3*(1-x-3*x^4)).
%p A143454 a := proc(k::nonnegint) local n,i,j; if k=0 then unapply (4^n,n) else 
               unapply ((Matrix(k+1, (i,j)-> if (i=j-1) or j=1 and i=1 then 1 elif 
               j=1 and i=k+1 then 3 else 0 fi)^(n+k))[1,1], n) fi end(3): seq (a(n), 
               n=0..47);
%Y A143454 3rd column of A143461.
%Y A143454 Sequence in context: A069212 A091290 A119256 this_sequence A065810 A123837 
               A125620
%Y A143454 Adjacent sequences: A143451 A143452 A143453 this_sequence A143455 A143456 
               A143457
%K A143454 nonn
%O A143454 0,2
%A A143454 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 16 2008