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%I #20 May 20 2023 19:22:51
%S 1,7,55,439,3511,28087,224695,1797559,14380471,115043767,920350135,
%T 7362801079,58902408631,471219269047,3769754152375,30158033218999,
%U 241264265751991,1930114126015927,15440913008127415,123527304065019319,988218432520154551,7905747460161236407
%N 7th row of number array A083064.
%C Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=10, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^(n-1)*charpoly(A,2). - _Milan Janjic_, Feb 21 2010
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F a(n) = (6*8^n+1)/7.
%F G.f. (1-2*x)/((1-8*x)(1-x)).
%F E.g.f. (6*exp(8*x)+exp(x))/7.
%F a(n) = 8*a(n-1)-1 with n>0, a(0)=1. - _Vincenzo Librandi_, Aug 08 2010
%F a(n) = 8^n - sum(8^i, i=0..n-1) for n>0. - _Bruno Berselli_, Jun 20 2013
%F a(n) = 1 + A125837(n+1). - _Alois P. Heinz_, May 20 2023
%t f[n_]:=8^n; lst={}; Do[a=f[n]; Do[a-=f[m],{m,n-1,1,-1}]; AppendTo[lst,a/8],{n,1,30}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2010 *)
%t LinearRecurrence[{9,-8},{1,7},20] (* _Harvey P. Dale_, Jul 18 2019 *)
%o (PARI) a(n)=(6*8^n+1)/7 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A083067, A083066, A125837.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Apr 21 2003
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