|
%I #12 Oct 09 2023 12:31:06
%S 1,4,7,10,13,16,19,22,34,55,85,124,172,229,295,397,562,817,1189,1705,
%T 2392,3277,4468,6154,8605,12172,17287,24463,34294,47698,66160,91975,
%U 128491,180352,253741,356623,499717,698197,974122,1359595,1900651
%N Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=6.
%C a(n) is also the number of length n quaternary words with at least 6 0-digits between any other digits.
%H Vincenzo Librandi, <a href="/A143457/b143457.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,3).
%F G.f.: 1/(x^6*(1-x-3*x^7)).
%p 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(6): seq (a(n), n=0..55);
%t Series[1/(1-x-3*x^7), {x, 0, 55}] // CoefficientList[#, x]& // Drop[#, 6]& (* _Jean-François Alcover_, Feb 13 2014 *)
%Y 6th column of A143461.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Aug 16 2008
|
