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

1,2

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).

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)

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 *)

Prog

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

Crossrefs

Sequence in context: A004957 A026352 A198084 * A342744 A057349 A087068

Adjacent sequences: A047396 A047397 A047398 * A047400 A047401 A047402

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved