A159329 Transform of the finite sequence (1, 0, -1) by the T_{1,1} transformation (see link).

2, 4, 9, 23, 54, 125, 290, 674, 1567, 3643, 8469, 19688, 45769, 106400, 247350, 575019, 1336757, 3107583, 7224254, 16794353, 39042134, 90761950, 210995935, 490506039, 1140288197, 2650848448, 6162474989, 14326016268, 33303947274

Offset: 0

Author

Richard Choulet, Apr 10 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. A159328.

Programs

Magma

I:=[9, 23, 54]; [2,4] 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

Mathematica

Join[{2,4}, LinearRecurrence[{3, -2, 1}, {9, 23, 54}, 50]] (* G. C. Greubel, Jun 26 2018 *)

PARI

x='x+O('x^30); Vec(2+4*x -x^2*(9-4*x+3*x^2)/(-1+3*x-2*x^2+x^3)) \\ G. C. Greubel, Jun 26 2018

Formula

O.g.f.: 2+4*x -x^2*(9-4*x+3*x^2) / ( -1+3*x-2*x^2+x^3 ).

a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=54 and for n>=2 a(n+3)=3*a(n+2)-2*a(n+1)+a(n).