A159331 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,1} transform (see link).

2, 4, 9, 23, 55, 126, 293, 680, 1581, 3676, 8546, 19867, 46185, 107367, 249598, 580245, 1348906, 3135826, 7289911, 16946987, 39396965, 91586832, 212913553, 494963960, 1150651606, 2674940451, 6218482101, 14456217007, 33606627270

Offset

0,1

Links

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

R. 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^4+z^6) + (z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3)).

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 9, with a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=55, a(5)=126, a(6)=293, a(7)=680, a(8)=1581.

Mathematica

Join[{2, 4, 9, 23, 55, 126}, LinearRecurrence[{3, -2, 1}, {293, 680, 1581}, 45]] (* G. C. Greubel, Jun 26 2018 *)

Prog

(PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4+z^6) + (z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 26 2018
(Magma) I:=[293, 680, 1581]; [2, 4, 9, 23, 55, 126] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 26 2018

Crossrefs

Cf. A159328, A159329, A159330.

Sequence in context: A159329 A159334 A159330 * A135346 A174283 A337516

Adjacent sequences: A159328 A159329 A159330 * A159332 A159333 A159334

Keyword

easy,nonn

Author

Richard Choulet, Apr 10 2009

Status

approved