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

0,2

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

Table of n, a(n) for n=0..21.

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

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

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 *)

Prog

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

Crossrefs

Cf. A083067, A083066, A125837.

Sequence in context: A370177 A122372 A342935 * A362299 A097189 A049028

Adjacent sequences: A083065 A083066 A083067 * A083069 A083070 A083071

Keyword

nonn,easy

Author

Paul Barry, Apr 21 2003

Status

approved