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%I #13 Aug 08 2019 18:52:28
%S 1,4,7,10,13,16,19,22,25,37,58,88,127,175,232,298,373,484,658,922,
%T 1303,1828,2524,3418,4537,5989,7963,10729,14638,20122,27694,37948,
%U 51559,69526,93415,125602,169516,229882,312964,426808,581485,790063,1070308,1447114
%N Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=7.
%C a(n) is also the number of length n quaternary words with at least 7 0-digits between any other digits.
%H Alois P. Heinz, <a href="/A143458/b143458.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 3).
%F G.f.: 1/(x^7*(1-x-3*x^8)).
%F a(0)=1, a(1)=4, a(2)=7, a(3)=10, a(4)=13, a(5)=16, a(6)=19, a(7)=22, a(n)=a(n-1)+3*a(n-8). - _Harvey P. Dale_, Jul 22 2013
%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(7): seq (a(n), n=0..60);
%t LinearRecurrence[{1,0,0,0,0,0,0,3},{1,4,7,10,13,16,19,22},50] (* _Harvey P. Dale_, Jul 22 2013 *)
%Y 7th column of A143461.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Aug 16 2008
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