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

Author

Richard Choulet, Apr 11 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A135364.

Programs

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

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 *)

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

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.