A111365 a(n) = 5*a(n-1) + 3*a(n-2) where a(0) = a(1) = 1.

1, 1, 8, 43, 239, 1324, 7337, 40657, 225296, 1248451, 6918143, 38336068, 212434769, 1177182049, 6523214552, 36147618907, 200307738191, 1109981547676, 6150830952953, 34084099407793, 188872989897824, 1046617247712499

Offset

0,3

References

Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (5, 3).

Formula

a(n)=A015536(n+1)-4*A015536(n). G.f.: (1-4x)/(1-5x-3x^2). [From R. J. Mathar, Jul 08 2009]

Example

a(2) = 5*a(1) + 3*a(0) = 5*1 + 3*1 = 8 which is the third term in the sequence.

Mathematica

Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{3, 5}, #]}]&, {1, 1}, 40]][[1]]  (* Harvey P. Dale, Mar 23 2011 *)

Crossrefs

Cf. A000045, A072264.

Sequence in context: A239033 A034361 A117617 * A199321 A346198 A144039

Adjacent sequences: A111362 A111363 A111364 * A111366 A111367 A111368

Keyword

nonn

Author

Parthasarathy Nambi, Nov 07 2005

Extensions

More terms from Robert G. Wilson v, Nov 10 2005

Status

approved