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URL: https://oeis.org/A102207

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A102207
a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3) with a(0) = 4, a(1) = 17, a(2) = 65.
1
4, 17, 65, 244, 912, 3405, 12709, 47432, 177020, 660649, 2465577, 9201660, 34341064, 128162597, 478309325, 1785074704, 6661989492, 24862883265, 92789543569, 346295291012, 1292391620480, 4823271190909, 18000693143157, 67179501381720, 250717312383724, 935689748153177
OFFSET
0,1
FORMULA
G.f.: (3*x-4)/((x-1)*(x^2-4*x+1)).
a(n) = (1/2)*(A001353(n+2) + 5*A001353(n+1) - 1). - Ralf Stephan, May 17 2007
a(n) = (1/12)*((27-17*sqrt(3))*(2-sqrt(3))^n+(27+17*sqrt(3))*(2+sqrt(3))^n-6). - Harvey P. Dale, Mar 15 2013
MAPLE
gfun[seriestolist](series((3*x-4)/((x-1)*(x^2-4*x+1)), x, 30))[];
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Dec 30 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jan 12 2005
STATUS
approved