A106570 a(n) = 4*a(n-1) + 3*a(n-2), with a(0)=0, a(1)=3.

0, 3, 12, 57, 264, 1227, 5700, 26481, 123024, 571539, 2655228, 12335529, 57307800, 266237787, 1236874548, 5746211553, 26695469856, 124020514083, 576168465900, 2676735405849, 12435447021096, 57771994301931, 268394318271012

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,3).

Formula

G.f.: 3*x/(1 - 4*x - 3*x^2).

a(n) = 4*a(n-1) + 3*a(n-2), a(0)=0, a(1)=3.

a(n) = 3*A015530(n).

Maple

a[0]:=0: a[1]:=3: for n from 2 to 24 do a[n]:=4*a[n-1]+3*a[n-2] od: seq(a[n], n=0..40);

Mathematica

LinearRecurrence[{4, 3}, {0, 3}, 41] (* G. C. Greubel, Sep 07 2021 *)

Prog

(Magma) [n le 2 select 3*(n-1) else 4*Self(n-1) + 3*Self(n-2): n in [1..41]]; // G. C. Greubel, Sep 07 2021
(Sage) [3*lucas_number1(n, 4, -3) for n in (0..40)] # G. C. Greubel, Sep 07 2021

Crossrefs

Cf. A015530, A106569.

Sequence in context: A001277 A334773 A192525 * A027140 A110309 A263667

Adjacent sequences: A106567 A106568 A106569 * A106571 A106572 A106573

Keyword

nonn,easy,less

Author

Roger L. Bagula, May 30 2005

Extensions

Edited by N. J. A. Sloane, Apr 30 2006

New name by G. C. Greubel, Sep 07 2021

Status

approved