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A083068 7th row of number array A083064. 4
1, 7, 55, 439, 3511, 28087, 224695, 1797559, 14380471, 115043767, 920350135, 7362801079, 58902408631, 471219269047, 3769754152375, 30158033218999, 241264265751991, 1930114126015927, 15440913008127415, 123527304065019319 (list; graph; refs; listen; history; text; internal format)
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..19.

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

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 *)

PROG

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

CROSSREFS

Cf. A083067, A083066.

Sequence in context: A015564 A070997 A122372 * A097189 A049028 A224274

Adjacent sequences:  A083065 A083066 A083067 * A083069 A083070 A083071

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Apr 21 2003

STATUS

approved

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Last modified September 23 15:54 EDT 2017. Contains 292361 sequences.