A132433 a(1) = 2; for n>=2, a(n) = 8*a(n-1) + 1.

2, 17, 137, 1097, 8777, 70217, 561737, 4493897, 35951177, 287609417, 2300875337, 18407002697, 147256021577, 1178048172617, 9424385380937, 75395083047497, 603160664379977, 4825285315039817, 38602282520318537, 308818260162548297, 2470546081300386377

Offset

1,1

Comments

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=7, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=(-1)^n*charpoly(A,-1). - Milan Janjic, Feb 21 2010

References

V. Reeben, The highly composite numbers by Srinivasa Ramanujan and the fundamental constants of physics. J. Madras Univ., Sect. B, 51 (Ramanujan's 100th birthday issue, with a Table of h.c.n.'s up to 10^102), (1988) 88-146.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: -x*(-2+x)/(-1+x)/(-1+8*x). - R. J. Mathar, Nov 14 2007

a(n) = 9*a(n-1) - 8*a(n-2) for n>2.

Mathematica

NestList[8#+1&, 2, 20] (* Harvey P. Dale, Aug 30 2021 *)

Prog

(PARI) Vec(x*(2 - x) / ((1 - x)*(1 - 8*x)) + O(x^30)) \\ Colin Barker, May 12 2017

Crossrefs

Cf. A132434.

Sequence in context: A037525 A037734 A201782 * A037557 A026941 A037493

Adjacent sequences: A132430 A132431 A132432 * A132434 A132435 A132436

Keyword

nonn,easy

Author

Vello Reeben (reeben(AT)ut.ee), Aug 25 2007

Status

approved