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A162270
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a(n) = ((5+sqrt(2))*(3+sqrt(2))^n + (5-sqrt(2))*(3-sqrt(2))^n)/2.
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1
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5, 17, 67, 283, 1229, 5393, 23755, 104779, 462389, 2040881, 9008563, 39765211, 175531325, 774831473, 3420269563, 15097797067, 66644895461, 294184793297, 1298594491555, 5732273396251, 25303478936621, 111694959845969
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OFFSET
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0,1
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COMMENTS
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Third binomial transform of A162396.
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 5, a(1) = 17.
G.f.: (5-13*x)/(1-6*x+7*x^2).
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MAPLE
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seq(coeff(series((5-13*x)/(1-6*x+7*x^2), x, n+1), x, n), n = 0..25); # Muniru A Asiru, Sep 28 2018
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MATHEMATICA
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LinearRecurrence[{6, -7}, {5, 17}, 30] (* Harvey P. Dale, Jun 04 2016 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+r)*(3+r)^n+(5-r)*(3-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 2009
(Magma) I:=[5, 17]; [n le 2 select I[n] else 6*Self(n-1) - 7*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 28 2018
(PARI) x='x+O('x^30); Vec((5-13*x)/(1-6*x+7*x^2)) \\ G. C. Greubel, Sep 28 2018
(GAP) a:=[5, 17];; for n in [3..25] do a[n]:=6*a[n-1]-7*a[n-2]; od; a; # Muniru A Asiru, Sep 28 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
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EXTENSIONS
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STATUS
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approved
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