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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,3).
Programs
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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
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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);
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Mathematica
LinearRecurrence[{4,3}, {0,3}, 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
Formula
Extensions
Edited by N. J. A. Sloane, Apr 30 2006
New name by G. C. Greubel, Sep 07 2021