A159340 Transform of the finite sequence (1, 0, -1) by the T_{0,1} transformation (see link).

2, 3, 6, 16, 38, 88, 204, 474, 1102, 2562, 5956, 13846, 32188, 74828, 173954, 404394, 940102, 2185472, 5080606, 11810976, 27457188, 63830218, 148387254, 344958514, 801931252, 1864263982, 4333887956, 10075067156, 23421689538, 54448822258

Offset

0,1

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)+((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 >= 5, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=38.

Maple

a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=38:for n from 2 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i), i=0..31);

Mathematica

Join[{2, 3}, LinearRecurrence[{3, -2, 1}, {6, 16, 38}, 49]] (* G. C. Greubel, Jun 25 2018 *)

Prog

(PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[6, 16, 38]; [2, 3] 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 25 2018

Crossrefs

Cf. A135364.

Sequence in context: A061220 A378076 A184322 * A369560 A159343 A159341

Adjacent sequences: A159337 A159338 A159339 * A159341 A159342 A159343

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved