A047399 Numbers that are congruent to {0, 3, 6} mod 8.

0, 3, 6, 8, 11, 14, 16, 19, 22, 24, 27, 30, 32, 35, 38, 40, 43, 46, 48, 51, 54, 56, 59, 62, 64, 67, 70, 72, 75, 78, 80, 83, 86, 88, 91, 94, 96, 99, 102, 104, 107, 110, 112, 115, 118, 120, 123, 126, 128, 131, 134, 136, 139, 142, 144, 147, 150, 152, 155, 158

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Programs

Magma

[Floor((8*n-6)/3): n in [1..60]]; // Vincenzo Librandi, Jul 11 2011

Maple

seq(floor((8*n-6)/3), n=1..52); # Gary Detlefs, Mar 07 2010

Mathematica

f[n_] := 3 n - Floor[n/3]; Array[f, 52, 0] (* Or *)
Cases[ Range[0, 136], n_ /; MatchQ[ Mod[n, 8], 0 | 3 | 6]] (* Robert G. Wilson v, Jul 10 2011 *)

Formula

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = floor((8*n-6)/3). [Gary Detlefs, Mar 07 2010]

a(n) = 3*n-floor(n/3). [Gary Detlefs, Jul 09 2011]

G.f. x^2*(3+3*x+2*x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = (24*n-21+3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)