A074581 a(n) = T(3n+1), where T(n) are tribonacci numbers A000073.

0, 2, 13, 81, 504, 3136, 19513, 121415, 755476, 4700770, 29249425, 181997601, 1132436852, 7046319384, 43844049029, 272809183135, 1697490356184, 10562230626642, 65720971788709, 408933139743937, 2544489349890656

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 24 2002

Keywords

• easy
• nonn

Comments

In general, the trisection of a third-order linear recurrence with signature (x,y,z) will result in a third-order recurrence with signature (x^3 + 3*x*y + 3*z, -3*x*y*z + y^3 - 3*z^2, z^3). - Gary Detlefs, May 29 2024

Links

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

Crossrefs

Cf. A000073.

Programs

Mathematica

CoefficientList[Series[(2*x-x^2)/(1-7*x+5*x^2-x^3), {x, 0, 40}], x]
LinearRecurrence[{7,-5,1},{0,2,13},30] (* Harvey P. Dale, Jul 22 2021 *)

Formula

a(n) = 7*a(n-1) - 5*a(n-2) + a(n-3), a(0)=0, a(1)=2, a(2)=13.

G.f.: (2*x - x^2)/(1 - 7*x + 5*x^2 - x^3). [corrected by Nguyen Tuan Anh, Jan 10 2025]

Extensions

Definition corrected by David Scambler, Oct 18 2010