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%I #17 Aug 03 2015 11:43:41
%S 1,9,28,119,451,1782,6931,27119,105868,413649,1615681,6311522,
%T 24654241,96306849,376200748,1469546399,5740457491,22423834422,
%U 87593763331,342165736199,1336595027068,5221113899769,20395130698081,79669083012482
%N Product of Lucas (A000204) and a Pell companion series (A001333).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 7, 2, -1).
%F a(n) = A000204(n) * A001333(n).
%F a(n) = 2*a(n-1)+7*a(n-2)+2*a(n-3)-a(n-4). G.f.: -x*(2*x^3-3*x^2-7*x-1) / (x^4-2*x^3-7*x^2-2*x+1). - _Colin Barker_, Oct 15 2013
%F 2* A085292(n) = A085293(n).
%t L[0] = 2; L[1] = 1; L[n] = L[n - 1] + L[n - 2]; P[0] = P[1] = 1; P[n_] := P[n] = 2P[n - 1] + P[n - 2]; Table[ L[n]P[n], {n, 1, 24}]
%t With[{nn=30},Rest[LinearRecurrence[{2,1},{1,1},nn]LucasL[Range[0,nn-1]]]] (* _Harvey P. Dale_, Apr 20 2012 *)
%t LinearRecurrence[{2, 7, 2, -1},{1, 9, 28, 119},24] (* _Ray Chandler_, Aug 03 2015 *)
%Y Cf. A085293, A000204, A001333, A002203.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Jun 24 2003
%E Edited and extended by _Robert G. Wilson v_, Jun 24 2003