PROG
(MAGMAMagma) I:=[0, 5, 7, 8]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, May 16 2012
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(MAGMAMagma) I:=[0, 5, 7, 8]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, May 16 2012
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Numbers m such that Lucas(m) mod 3 = 2. - Bruno Berselli, Oct 19 2017
G.f.: x^2*(5+2*x+x^2)/((1-x)^2*(1+x+x^2)). [_- _Colin Barker_, May 14 2012]
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. [_- _Vincenzo Librandi_, May 16 2012]
a(n) = (24*n - 12 + 3*cos(2*n*Pi/3) - 7*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k3*k) = 8k8*k-1, a(3k3*k-1) = 8k8*k-3, a(3k3*k-2) = 8k8*k-8. (End)
Select[Range[0, 300], MemberQ[{0, 5, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, May 16 2012 *)
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0, 5, 7, 8, 13, 15, 16, 21, 23, 24, 29, 31, 32, 37, 39, 40, 45, 47, 48, 53, 55, 56, 61, 63, 64, 69, 71, 72, 77, 79, 80, 85, 87, 88, 93, 95, 96, 101, 103, 104, 109, 111, 112, 117, 119, 120, 125, 127, 128, 133, 135, 136, 141, 143, 144, 149, 151, 152, 157, 159
<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. [Vincenzo Librandi, May 16 2012]
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = (24*n-12+3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-8. (End)
A047477:=n->(24*n-12+3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047477(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
Select[Range[0, 300], MemberQ[{0, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)
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<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
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