A085292 Product of Lucas (A000204) and a Pell companion series (A001333).

1, 9, 28, 119, 451, 1782, 6931, 27119, 105868, 413649, 1615681, 6311522, 24654241, 96306849, 376200748, 1469546399, 5740457491, 22423834422, 87593763331, 342165736199, 1336595027068, 5221113899769, 20395130698081, 79669083012482

Offset: 1

Author

Gary W. Adamson, Jun 24 2003

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2, 7, 2, -1).

Crossrefs

Cf. A085293, A000204, A001333, A002203.

Programs

Mathematica

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}]
With[{nn=30},Rest[LinearRecurrence[{2,1},{1,1},nn]LucasL[Range[0,nn-1]]]] (* Harvey P. Dale, Apr 20 2012 *)
LinearRecurrence[{2, 7, 2, -1},{1, 9, 28, 119},24] (* Ray Chandler, Aug 03 2015 *)

Formula

a(n) = A000204(n) * A001333(n).

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

2* A085292(n) = A085293(n).

Extensions

Edited and extended by Robert G. Wilson v, Jun 24 2003