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Search: id:A140781
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| A140781 |
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a(n) = 10*a(n-1) - a(n-2). |
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+0
1
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| 1, 2, 19, 188, 1861, 18422, 182359, 1805168, 17869321, 176888042, 1751011099, 17333222948, 171581218381
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OFFSET
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0,2
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COMMENT
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A140780 has the same recursion rule but starts (1, 3, 29,...).
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) = 2. a(n) = term (1,1) in X^n, where X = the 2x2 matrix [2,3; 5,8].
a(n) = (-1/8)*[5+2*sqrt(6)]^n*sqrt(6)+(1/8)*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(5) = 18422 = 10*a(4) - a(3) = 10*1861 - 188.
a(3) = 188 = term (1,1) of X^3.
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CROSSREFS
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Cf. A140780.
Adjacent sequences: A140778 A140779 A140780 this_sequence A140782 A140783 A140784
Sequence in context: A037742 A037637 A124262 this_sequence A128970 A145104 A114016
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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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