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A140780
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a(n) = 10*a(n-1) - a(n-2).
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1
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1, 3, 29, 287, 2841, 28123, 278389, 2755767, 27279281, 270037043, 2673091149, 26460874447, 261935653321, 2592895658763, 25667020934309, 254077313684327, 2515106115908961, 24896983845405283, 246454732338143869, 2439650339536033407, 24150048663022190201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)/a(n-1) tends to 2*sqrt(6) + 5 = 9.8989794855...
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FORMULA
| 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 (paoloplava(AT)gmail.com), Jun 06 2008
G.f.: (1-7*x)/(x^2-10*x+1) [From Harvey P. Dale, Jan 19 2012]
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EXAMPLE
| a(3) = 287 = 10*a(2) - a(1) = 10*29 - 3.
a(3) = 287 = term (1,1) in X^3.
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MATHEMATICA
| LinearRecurrence[{10, -1}, {1, 3}, 30] (* From Harvey P. Dale, Jan 19 2012 *)
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CROSSREFS
| Sequence in context: A026130 A026159 A025186 * A002669 A112711 A155651
Adjacent sequences: A140777 A140778 A140779 * A140781 A140782 A140783
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2008
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EXTENSIONS
| More terms from Harvey P. Dale, Jan 19 2012
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