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A132433
a(1) = 2; for n>=2, a(n) = 8*a(n-1) + 1.
2
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.
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
KEYWORD
nonn,easy
AUTHOR
Vello Reeben (reeben(AT)ut.ee), Aug 25 2007
STATUS
approved