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A106570
a(n) = 4*a(n-1) + 3*a(n-2), with a(0)=0, a(1)=3.
1
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
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
Sequence in context: A001277 A334773 A192525 * A027140 A110309 A263667
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