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

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. A034943.

Programs

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

Mathematica

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

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

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