A159337 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,0} transformation (see link).

1, 2, 4, 11, 27, 61, 141, 328, 763, 1774, 4124, 9587, 22287, 51811, 120446, 280003, 650928, 1513224, 3517819, 8177937, 19011397, 44196136, 102743551, 238849778, 555258368, 1290819099, 3000790339, 6975991187, 16217211982, 37700443911

Offset

0,2

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)+(z/(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)=1, a(1)=2,a(2)=4, a(3)=11, a(4)=27, a(5)=61, a(6)=141.

Maple

a(0):=1: a(1):=2:a(2):=4: a(3):=11:a(4):=27:a(5):=61:a(6):=141: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[{1, 2, 4, 11}, LinearRecurrence[{3, -2, 1}, {27, 61, 141}, 997]] (* G. C. Greubel, Jun 25 2018 *)

Prog

(PARI) z='z+O('z^50); 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))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[27, 61, 141]; [1, 2, 4, 11] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..50]]; // G. C. Greubel, Jun 25 2018

Crossrefs

Cf. A159336.

Sequence in context: A090899 A159338 A159339 * A243736 A316772 A123440

Adjacent sequences: A159334 A159335 A159336 * A159338 A159339 A159340

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved