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A138513
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a(n) = 8*a(n-1) - 5*a(n-2).
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1
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1, 3, 19, 137, 1001, 7323, 53579, 392017, 2868241, 20985843, 153545539, 1123435097, 8219753081, 60140849163, 440028027899, 3219519977377, 23556019679521, 172350557549283, 1261024361996659, 9226442108226857
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Rightmost digit of each term forms a cycle with period 4: 1, 3, 9, 7,...(repeat)...
a(n)/a(n-1) tends to (4 + sqrt(11)) = 7.31662479...
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..500
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FORMULA
| a(n) = 8*a(n-1) - 5*a(n-2), n> 2; given a(1) = 1, a(2) = 3. a(n) = upper left term of the 2 X 2 matrix [1,2; 1,7]^n * [1,0].
O.g.f.: -x*(-1+5*x)/(1-8*x+5*x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 12 2008
a(n)=[(3sqrt(11)/22+1/2][4-sqrt(11)]^n + [(-3sqrt(11)/22+1/2][4+sqrt(11)]^n - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2008
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EXAMPLE
| a(5) = 1001 = 8*a(4) - 5*a(3) = 8*137 - 5*19.
a(5) = 1001 = upper left term in [1,2; 1,7]^5.
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MAPLE
| a[1]:=1: a[2]:=3: for n from 3 to 25 do a[n]:=8*a[n-1]-5*a[n-2] end do: seq(a[n], n=1..20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2008
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CROSSREFS
| Sequence in context: A091346 A035086 A105797 * A094661 A094662 A115750
Adjacent sequences: A138510 A138511 A138512 * A138514 A138515 A138516
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 22 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 12 2008
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