A159330 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,1} transformation (see link).

2, 4, 9, 23, 55, 126, 292, 679, 1579, 3671, 8534, 19839, 46120, 107216, 249247, 579429, 1347009, 3131416, 7279659, 16923154, 39341560, 91458031, 212614127, 494267879, 1149033414, 2671178611, 6209736884, 14435886844, 33559365375, 78016059321, 181365334057

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/(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 >= 7, with a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=55, a(5)=126, a(6)=292.

Mathematica

Join[{2, 4, 9, 23}, LinearRecurrence[{3, -2, 1}, {55, 126, 292}, 47]] (* G. C. Greubel, Jun 26 2018 *)

Prog

(PARI) my(z='z+O('z^31)); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + 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:=[55, 126, 292]; [2, 4, 9, 23] 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.

Sequence in context: A278691 A159329 A159334 * A159331 A135346 A174283

Adjacent sequences: A159327 A159328 A159329 * A159331 A159332 A159333

Keyword

easy,nonn,changed

Author

Richard Choulet, Apr 10 2009

Status

approved