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%I #22 Sep 08 2022 08:45:10
%S 1,6,41,286,2001,14006,98041,686286,4804001,33628006,235396041,
%T 1647772286,11534406001,80740842006,565185894041,3956301258286,
%U 27694108808001,193858761656006,1357011331592041,9499079321144286
%N 6th row of number array A083064.
%C Binomial transform of A052934 - _Paul Barry_, Apr 30 2003
%C Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=9, (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). [From _Milan Janjic_, Feb 21 2010]
%H Vincenzo Librandi, <a href="/A083067/b083067.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F a(n) = (5*7^n+1)/6.
%F G.f.: (1-2*x)/((1-7*x)*(1-x)).
%F E.g.f.: (5*exp(7*x)+exp(x))/6.
%F a(n) = 7*a(n-1)-1 with a(0)=1. - _Vincenzo Librandi_, Aug 08 2010
%F a(n) = 8*a(n-1)-7*a(n-2). - _Vincenzo Librandi_, Nov 06 2011
%F a(n) = 7^n - sum(7^i, i=0..n-1) for n>0. [_Bruno Berselli_, Jun 20 2013]
%t f[n_]:=7^n; lst={}; Do[a=f[n]; Do[a-=f[m],{m,n-1,1,-1}]; AppendTo[lst,a/7],{n,1,30}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2010 *)
%o (Magma) [(5*7^n+1)/6: n in [0..30]]; // _Vincenzo Librandi_, Nov 06 2011
%Y Cf. A083066, A083068.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Apr 21 2003
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