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Search: id:A138322
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| A138322 |
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a(n) = 5*a(n-1) + 10*a(n-2). |
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+0
1
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| 1, 15, 85, 575, 3725, 24375, 159125, 1039375, 6788125, 44334375, 289553125, 1891109375, 12351078125, 80666484375, 526843203125, 3440880859375, 22472836328125, 146772990234375, 958593314453125, 6260696474609375
(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 6.53112887... = (5 + sqrt(65))/2
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FORMULA
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a(n), n>1 = 5*a(n-1) + 10*a(n-2), given a(0) = 1, a(1) = 15. [a(n), a(n+1)] = the 2 X 2 matrix [0,1; 10,5]^n * [1,15]
O.g.f.: (-1-10*x)/(-1+5*x+10*x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 15 2008
a(n)=5/26*sqrt(65)*(5/2+1/2*sqrt(65))^n+1/2*(5/2-1/2*sqrt(65))^n-5/26*(5/2-1/2 *sqrt(65))^n*sqrt(65)+1/2*(5/2+1/2*sqrt(65))^n, where n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 03 2008
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EXAMPLE
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a(5) = 24375 = 5*a(4) + 10*a(3) = 5*3725 + 10*575.
[a(3), a(4)] = [575,3725] = [0,1; 10,5]^3 * [1,15].
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CROSSREFS
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Sequence in context: A160599 A091286 A064058 this_sequence A164541 A145789 A010822
Adjacent sequences: A138319 A138320 A138321 this_sequence A138323 A138324 A138325
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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), Mar 14 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 15 2008
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