A019481 a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3) (agrees with A019480 for n <= 19 only).

4, 12, 37, 115, 358, 1115, 3473, 10818, 33697, 104963, 326950, 1018419, 3172281, 9881362, 30779529, 95875387, 298642966, 930245227, 2897627873, 9025842914, 28114666161, 87574585651, 272786737286, 849705465187, 2646753961545, 8244393875250

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• R. K. Guy, personal communication.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,1,-2)

Programs

Magma

I:=[4, 12, 37]; [n le 3 select I[n] else 3*Self(n-1)+Self(n-2)-2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jan 18 2017

Mathematica

LinearRecurrence[{3,1, -2}, {4, 12, 37}, 30] (* Harvey P. Dale, Jan 17 2017 *)

Formula

From R. J. Mathar, Aug 22 2008: (Start)

O.g.f.: (4 - 3*x^2)/(1 - 3*x - x^2 + 2*x^3).

a(n) = 4*A100058(n) - 3*A100058(n-2). (End)