A135139 a(n) = 5*a(n-2) + 2*a(n-3).

1, 2, 4, 12, 24, 68, 144, 388, 856, 2228, 5056, 12852, 29736, 74372, 174384, 431332, 1020664, 2505428, 5965984, 14568468, 34840776, 84774308, 203340816, 493553092, 1186252696, 2874447092, 6918369664, 16744740852, 40340742504, 97560443588

Offset: 0

Author

Paul Curtz, Feb 13 2008

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 5, 2).

Crossrefs

Cf. A135138.

Programs

Mathematica

a = {1, 2, 4}; Do[AppendTo[a, 5*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* Stefan Steinerberger, Feb 15 2008 *)
LinearRecurrence[{0,5,2},{1,2,4},30] (* Harvey P. Dale, May 25 2012 *)

Formula

From R. J. Mathar, Feb 15 2008: (Start)

O.g.f.: 4*(x-2)/(7*(x^2+2*x-1)) - 1/(7*(1+2*x)).

a(n) = (4*A078343(n+1)-(-2)^n)/7.

a(n) = A135138(n+2) + 2*A135138(n+1) - A135138(n). (End)

Extensions

More terms from R. J. Mathar and Stefan Steinerberger, Feb 15 2008