A159328 Transform of 1 by the T_{1,1} transformation (see link)

2, 4, 10, 24, 56, 130, 302, 702, 1632, 3794, 8820, 20504, 47666, 110810, 257602, 598852, 1392162, 3236384, 7523680, 17490434, 40660326, 94523790, 219741152, 510836202, 1187550092, 2760719024, 6417893090, 14919791314, 34684306786

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/(1-3*z+2*z^2-z^3))+((1-z+z^2)/(1-3*z+2*z^2-z^3)).

a(0), a(1)=4, a(2)=10 and for n>=0 a(n+3)=3*a(n+2)-2*a(n+1)+a(n).

a(n) = 2*A034943(n+2). - R. J. Mathar, Feb 19 2016

Mathematica

LinearRecurrence[{3, -2, 1}, {2, 4, 10}, 30] (* Harvey P. Dale, May 10 2016 *)

Prog

(PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*1+(z/(1-3*z+2*z^2-z^3))+((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 26 2018
(Magma) I:=[2, 4, 10]; [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

Crossrefs

Cf. A034943.

Sequence in context: A275447 A095214 A002525 * A190587 A190794 A052912

Adjacent sequences: A159325 A159326 A159327 * A159329 A159330 A159331

Keyword

easy,nonn

Author

Richard Choulet, Apr 10 2009

Status

approved