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A083067 6th row of number array A083064. 5
1, 6, 41, 286, 2001, 14006, 98041, 686286, 4804001, 33628006, 235396041, 1647772286, 11534406001, 80740842006, 565185894041, 3956301258286, 27694108808001, 193858761656006, 1357011331592041, 9499079321144286 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A052934 - Paul Barry, Apr 30 2003

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]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-7).

FORMULA

a(n) = (5*7^n+1)/6.

G.f.: (1-2*x)/((1-7*x)*(1-x)).

E.g.f.: (5*exp(7*x)+exp(x))/6.

a(n) = 7*a(n-1)-1 with a(0)=1. - Vincenzo Librandi, Aug 08 2010

a(n) = 8*a(n-1)-7*a(n-2). - Vincenzo Librandi, Nov 06 2011

a(n) = 7^n - sum(7^i, i=0..n-1) for n>0. [Bruno Berselli, Jun 20 2013]

MATHEMATICA

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 *)

PROG

(MAGMA) [(5*7^n+1)/6: n in [0..30]]; // Vincenzo Librandi, Nov 06 2011

CROSSREFS

Cf. A083066, A083068.

Sequence in context: A049685 A196954 A122371 * A000402 A186654 A152107

Adjacent sequences:  A083064 A083065 A083066 * A083068 A083069 A083070

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Apr 21 2003

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)