A108136 a(1)=1; a(2)=1; a(3)=1; a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3).

1, 1, 1, 6, 21, 76, 276, 1001, 3631, 13171, 47776, 173301, 628626, 2280256, 8271321, 30003101, 108832201, 394774126, 1431989881, 5194350096, 18841804176, 68346102601, 247916266251, 899282808131, 3262027059496, 11832563061001

Offset: 1

Author

Roger L. Bagula, Jun 05 2005

Keywords

• nonn
• easy

Comments

Length of steps in the 3-symbol substitution 1->{2}, 2->{3}, 3->{1,2,2,3,3,3} with characteristic polynomial: x^3 - 3*x^2 - 2*x - 1.

No term is divisible by 5. - Vladimir Joseph Stephan Orlovsky, Mar 24 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (3, 2, 1).

Programs

Mathematica

LinearRecurrence[{3, 2, 1}, {1, 1, 1}, 30]

Formula

From R. J. Mathar, Oct 14 2008: (Start)

G.f.: x*(1 - 2*x - 4*x^2)/(1 - 3*x - 2*x^2 - x^3).

a(n) = A108153(n) - 2*A108153(n-1) - 4*A108153(n-2). (End)