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A102207
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a(n) = 5a(n-1) - 5a(n-2) + a(n-3) with a(0) = 4, a(1) = 17, a(2) = 65.
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1
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4, 17, 65, 244, 912, 3405, 12709, 47432, 177020, 660649, 2465577, 9201660, 34341064, 128162597, 478309325, 1785074704, 6661989492, 24862883265, 92789543569, 346295291012, 1292391620480, 4823271190909, 18000693143157
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (3x-4)/((x-1)(x^2-4x+1))
a(n)=1/12*((3-7*Sqrt[3])*(2-Sqrt[3])^n+(3+7*Sqrt[3])*(2+Sqrt[3])^n-6). - Harvey P. Dale, Mar 15 2013
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MATHEMATICA
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a[0] = 4; a[1] = 17; a[2] = 65; a[n_] := a[n] = 5a[n - 1] - 5a[n - 2] + a[n - 3]; Table[ a[n], {n, 0, 22}] (* Or *)
CoefficientList[ Series[(3x - 4)/((x - 1)(x^2 - 4x + 1)), {x, 0, 22}], x] (* Robert G. Wilson v, Jan 12 2005 *)
LinearRecurrence[{5, -5, 1}, {4, 17, 65}, 30] (* or *) With[{c=Sqrt[3]}, Table[ Simplify[ ((3-7c)(2-c)^x+(2+c)^x (3+7c)-6)/12], {x, 30}]] (* Harvey P. Dale, Mar 15 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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