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A132433
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a(1) = 2; for n>=2, a(n) = 8*a(n-1)+1.
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1
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2, 17, 137, 1097, 8777, 70217, 561737, 4493897, 35951177, 287609417, 2300875337, 18407002697, 147256021577, 1178048172617, 9424385380937, 75395083047497, 603160664379977, 4825285315039817, 38602282520318537, 308818260162548297, 2470546081300386377
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Quadratic radical circle dividers in multi-step manner, 17 being the famous Gauss discovery, 137 being my discovery. Also the core of the physical fine structure constant.
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). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
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REFERENCES
| Reeben,V.: 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.
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FORMULA
| G.f.: -x*(-2+x)/(-1+x)/(-1+8*x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=-1/7+(15/7)*8^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 08 2008
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CROSSREFS
| Cf. A132434.
Sequence in context: A037525 A037734 A201782 * A037557 A026941 A037493
Adjacent sequences: A132430 A132431 A132432 * A132434 A132435 A132436
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KEYWORD
| nonn
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AUTHOR
| Vello Reeben (reeben(AT)ut.ee), Aug 25 2007
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