A102207 a(n) = 5a(n-1) - 5a(n-2) + a(n-3) with a(0) = 4, a(1) = 17, a(2) = 65.

4, 17, 65, 244, 912, 3405, 12709, 47432, 177020, 660649, 2465577, 9201660, 34341064, 128162597, 478309325, 1785074704, 6661989492, 24862883265, 92789543569, 346295291012, 1292391620480, 4823271190909, 18000693143157

Offset: 0

Author

Creighton Dement, Dec 30 2004

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (5, -5, 1).

Crossrefs

Cf. A061278, A092184, A001834, A001353, A102206.

Programs

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 *)

Formula

G.f.: (3x-4)/((x-1)(x^2-4x+1))

(1/2) [A001353(n+1) + 5*A001353(n) - 1 ]. - Ralf Stephan, May 17 2007

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

Extensions

More terms from Robert G. Wilson v, Jan 12 2005