|
%I #23 Oct 09 2023 12:30:12
%S 1,4,7,10,13,16,28,49,79,118,166,250,397,634,988,1486,2236,3427,5329,
%T 8293,12751,19459,29740,45727,70606,108859,167236,256456,393637,
%U 605455,932032,1433740,2203108,3384019,5200384,7996480,12297700,18907024
%N Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=4.
%C a(n) is also the number of length n quaternary words with at least 4 0-digits between any other digits.
%C The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=9, 4*a(n-9) equals the number of 4-colored compositions of n with all parts >=5, such that no adjacent parts have the same color. - _Milan Janjic_, Nov 27 2011
%H Vincenzo Librandi, <a href="/A143455/b143455.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,3).
%F G.f.: 1/(x^4*(1-x-3*x^5)).
%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(4): seq(a(n), n=0..50);
%t Series[1/(1-x-3*x^5), {x, 0, 50}] // CoefficientList[#, x]& // Drop[#, 4]& (* _Jean-François Alcover_, Feb 13 2014 *)
%Y 4th column of A143461.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Aug 16 2008
|
