A083067 6th row of number array A083064.

1, 6, 41, 286, 2001, 14006, 98041, 686286, 4804001, 33628006, 235396041, 1647772286, 11534406001, 80740842006, 565185894041, 3956301258286, 27694108808001, 193858761656006, 1357011331592041, 9499079321144286

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: A370176 A196954 A122371 * A000402 A186654 A152107

Adjacent sequences: A083064 A083065 A083066 * A083068 A083069 A083070

Keyword

nonn,easy

Author

Paul Barry, Apr 21 2003

Status

approved