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

0,3

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

Table of n, a(n) for n=0..23.

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

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

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 *)

Crossrefs

Cf. A009943, A120987.

Sequence in context: A218992 A190974 A027279 * A355347 A254660 A093738

Adjacent sequences: A099461 A099462 A099463 * A099465 A099466 A099467

Keyword

easy,nonn

Author

Paul Barry, Oct 16 2004

Status

approved