PROG
(MAGMAMagma) I:=[1, 5, 7, 9]; [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:=[1, 5, 7, 9]; [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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a(n) = 2*(n + floor((n+1)/3)) - 1. - Wolfdieter Lang, Sep 11 2021
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1, 5, 7, 9, 13, 15, 17, 21, 23, 25, 29, 31, 33, 37, 39, 41, 45, 47, 49, 53, 55, 57, 61, 63, 65, 69, 71, 73, 77, 79, 81, 85, 87, 89, 93, 95, 97, 101, 103, 105, 109, 111, 113, 117, 119, 121, 125, 127, 129, 133, 135, 137, 141, 143, 145, 149, 151, 153, 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-9-4*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-7. (End)
A047478:=n->(24*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047478(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
Select[Range[0, 300], MemberQ[{1, 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).