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A090249
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a(n) = 28a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 28.
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3
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2, 28, 782, 21868, 611522, 17100748, 478209422, 13372763068, 373959156482, 10457483618428, 292435582159502, 8177738816847628, 228684251289574082, 6394981297291226668, 178830792072864772622, 5000867196742922406748
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OFFSET
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0,1
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COMMENTS
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a(n+1)/a(n) converges to (14+sqrt(195)) =27.96424004... Lim a(n)/a(n+1) as n approaches infinity = 0.03575995... = 1/(14+sqrt(195)) = (14-sqrt(195)). Lim a(n+1)/a(n) as n approaches infinity = 27.96424004... = (14+sqrt(195)) = 1/(14-sqrt(195)). Lim a(n)/a(n+1) = 28 - Lim a(n+1)/a(n).
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LINKS
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FORMULA
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a(n) = 28a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 28. a(n) = (14+sqrt(195))^n + (14-sqrt(195))^n. (a(n))^2 =a(2n)+2.
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EXAMPLE
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a(4) = 611522 = 28a(3) - a(2) = 28*21868 - 782 =(14+sqrt(195))^4 + (14-sqrt(195))^4 =611521.999998364 + 0.000001635 =611522.
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MATHEMATICA
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a[0] = 2; a[1] = 28; a[n_] := 28a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)
LinearRecurrence[{28, -1}, {2, 28}, 20] (* or *) CoefficientList[ Series[ (2-28x)/(x^2-28x+1), {x, 0, 20}], x] (* Harvey P. Dale, Jun 25 2011 *)
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PROG
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(Sage) [lucas_number2(n, 28, 1) for n in range(0, 16)] # Zerinvary Lajos, Jun 27 2008
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 24 2004
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EXTENSIONS
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STATUS
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approved
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