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

1,2

Links

Table of n, a(n) for n=1..24.

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

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).

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 *)

Crossrefs

Cf. A085293, A000204, A001333, A002203.

Sequence in context: A053819 A294287 A349547 * A198059 A181090 A073706

Adjacent sequences: A085289 A085290 A085291 * A085293 A085294 A085295

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 24 2003

Extensions

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

Status

approved