A159341 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).

2, 3, 6, 16, 39, 89, 206, 479, 1114, 2590, 6021, 13997, 32539, 75644, 175851, 408804, 950354, 2209305, 5136011, 11939777, 27756614, 64526299, 150005446, 348720354, 810676469, 1884594145, 4381149851, 10184937732, 23677107639, 55042597304

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+z^4) + ((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)=3, a(2)=6, a(3)=16, a(4)=39, a(5)=89, a(6)=206.

Maple

a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:a(5):=89:a(6):=206:for n from 4 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, 6, 16}, LinearRecurrence[{3, -2, 1}, {39, 89, 206}, 47]] (* 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+z^4) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[39, 89, 206]; [2, 3, 6, 16] 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, A159340.

Sequence in context: A159340 A369560 A159343 * A159342 A089872 A006402

Adjacent sequences: A159338 A159339 A159340 * A159342 A159343 A159344

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved