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A147959
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a(n) = ((8 + sqrt(2))^n + (8 - sqrt(2))^n)/2.
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4
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1, 8, 66, 560, 4868, 43168, 388872, 3545536, 32618512, 302072960, 2810819616, 26244590336, 245642629184, 2303117466112, 21620036448384, 203127300275200, 1909594544603392, 17959620096591872, 168959059780059648
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 16*a(n-1) - 62*a(n-2), n > 1; a(0)=1, a(1)=8.
G.f.: (1 - 8*x)/(1 - 16*x + 62*x^2).
a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2k)*2^(n-k))/8^n. (End)
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EXAMPLE
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a(3) = ((8 + sqrt(2))^3 + (8 - sqrt(2))^3)/2
= (8^3 + 3*8^2*sqrt(2) + 3*8*2 + 2*sqrt(2)
+ 8^3 - 3*8^2*sqrt(2) + 3*8*2 - 2*sqrt(2))/2
= 8^3 + 3*8*2
= 560.
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MATHEMATICA
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LinearRecurrence[{16, -62}, {1, 8}, 50] (* G. C. Greubel, Aug 17 2018 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); S:=[ ((8+r2)^n+(8-r2)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 19 2008
(PARI) x='x+O('x^30); Vec((1-8*x)/(1-16*x+62*x^2)) \\ G. C. Greubel, Aug 17 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), Nov 17 2008
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EXTENSIONS
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STATUS
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approved
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