A099464 Trisection of tribonacci numbers.

0, 1, 7, 44, 274, 1705, 10609, 66012, 410744, 2555757, 15902591, 98950096, 615693474, 3831006429, 23837527729, 148323355432, 922906855808, 5742568741225, 35731770264967, 222332455004452, 1383410902447554, 8607945812375585, 53560898629395777, 333269972246340068

Offset: 0

Author

Paul Barry, Oct 16 2004

Keywords

• easy
• nonn

Comments

Let A = [1,1,1; 2,4,3; 1,2,2]. a(n) is given by the (1,2) term in A^n.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-5,1).

Crossrefs

Cf. A009943, A120987.

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <1|-5|7>>^n)[3, 1]:
seq(a(n), n=0..30);  # Alois P. Heinz, Dec 11 2015

Mathematica

LinearRecurrence[{7,-5,1},{0,1,7},30] (* Harvey P. Dale, Jan 14 2016 *)

Formula

G.f.: x/(1-7*x+5*x^2-x^3).

a(n) = 7a(n-1) -5a(n-2) +a(n-3).

a(n) = A000073(3n).

a(n) = Sum_{i>=n-1} A120987(i,n-1) for n>0. - Alois P. Heinz, Dec 11 2015