A159336 Transform of the finite sequence (1, 0, -1) by the T_{1,0} transformation (see link).

1, 2, 4, 11, 26, 60, 139, 323, 751, 1746, 4059, 9436, 21936, 50995, 118549, 275593, 640676, 1489391, 3462414, 8049136, 18711971, 43500055, 101125359, 235087938, 546513151, 1270488936, 2953528444, 6866120611, 15961793881, 37106668865

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Richard Choulet, Curtz-like transformation.

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

Formula

O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+(z/(1-3*z+2*z^2-z^3)).

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 5, with a(0)=1, a(1)=2, a(2)=4, a(3)=11, a(4)=26.

Mathematica

Join[{1, 2}, LinearRecurrence[{3, -2, 1}, {4, 11, 26}, 49]] (* G. C. Greubel, Jun 25 2018 *)

Prog

(PARI) z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+(z/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[4, 11, 26]; [1, 2] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..50]]; // G. C. Greubel, Jun 25 2018

Crossrefs

Cf. A034943.

Sequence in context: A122121 A368412 A080009 * A240571 A151257 A148117

Adjacent sequences: A159333 A159334 A159335 * A159337 A159338 A159339

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved