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A143456 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=5. 3


%S 1,4,7,10,13,16,19,31,52,82,121,169,226,319,475,721,1084,1591,2269,

%T 3226,4651,6814,10066,14839,21646,31324,45277,65719,95917,140434,

%U 205372,299344,435175,632332,920083,1341385,1957501,2855533,4161058,6058054

%N Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=5.

%C a(n) is also the number of length n quaternary words with at least 5 0-digits between any other digits.

%H Vincenzo Librandi, <a href="/A143456/b143456.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1/(x^5*(1-x-3*x^6)).

%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(5): seq(a(n), n=0..52);

%t Series[1/(1-x-3*x^6), {x, 0, 52}] // CoefficientList[#, x]& // Drop[#, 5]& (* _Jean-François Alcover_, Feb 13 2014 *)

%Y 5th column of A143461.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Aug 16 2008

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Last modified December 4 19:06 EST 2022. Contains 358563 sequences. (Running on oeis4.)