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Search: id:A140780
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| A140780 |
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a(n) = 10*a(n-1) - a(n-2). |
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+0
2
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| 1, 3, 29, 287, 2841, 28123, 278389, 2755767, 27279281, 270037043, 2673091149, 26460874447, 261935653321
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)/a(n-1) tends to 2*sqrt(6) + 5 = 9.8989794855...
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FORMULA
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a(n) = 10*a(n-1), - a(n-2), n>1; given a(0) = 1, a(1) = 3. Term (1,1) in X^n where X = the 2x2 matrix [3,4; 5,7].
a(n) = (-1/12)*[5+2*sqrt(6)]^n*sqrt(6)+(1/12)*sqrt(6)*[5-2*sqrt(6)]^n+(1/2)*[5+2*sqrt(6)]^n+(1 /2)*[5-2*sqrt(6)]^n, with n >= 0 - Paolo P. Lava (ppl(AT)spl.at), Jun 06 2008
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EXAMPLE
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a(3) = 287 = 10*a(2) - a(1) = 10*29 - 3.
a(3) = 287 = term (1,1) in X^3.
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CROSSREFS
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Adjacent sequences: A140777 A140778 A140779 this_sequence A140781 A140782 A140783
Sequence in context: A026130 A026159 A025186 this_sequence A002669 A112711 A001947
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2008
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