A083068 7th row of number array A083064.

1, 7, 55, 439, 3511, 28087, 224695, 1797559, 14380471, 115043767, 920350135, 7362801079, 58902408631, 471219269047, 3769754152375, 30158033218999, 241264265751991, 1930114126015927, 15440913008127415, 123527304065019319, 988218432520154551, 7905747460161236407

Offset: 0

Author

Paul Barry, Apr 21 2003

Keywords

• nonn
• easy

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A083067, A083066, A125837.

Programs

Mathematica

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 *)
LinearRecurrence[{9,-8},{1,7},20] (* Harvey P. Dale, Jul 18 2019 *)

PARI

a(n)=(6*8^n+1)/7 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (6*8^n+1)/7.

G.f. (1-2*x)/((1-8*x)(1-x)).

E.g.f. (6*exp(8*x)+exp(x))/7.

a(n) = 8*a(n-1)-1 with n>0, a(0)=1. - Vincenzo Librandi, Aug 08 2010

a(n) = 8^n - sum(8^i, i=0..n-1) for n>0. - Bruno Berselli, Jun 20 2013

a(n) = 1 + A125837(n+1). - Alois P. Heinz, May 20 2023