A047399 - OEIS

%I #25 Sep 08 2022 08:44:57

%S 0,3,6,8,11,14,16,19,22,24,27,30,32,35,38,40,43,46,48,51,54,56,59,62,

%T 64,67,70,72,75,78,80,83,86,88,91,94,96,99,102,104,107,110,112,115,

%U 118,120,123,126,128,131,134,136,139,142,144,147,150,152,155,158

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

%H Vincenzo Librandi, <a href="/A047399/b047399.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

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

%F a(n) = floor((8*n-6)/3). [_Gary Detlefs_, Mar 07 2010]

%F a(n) = 3*n-floor(n/3). [_Gary Detlefs_, Jul 09 2011]

%F G.f. x^2*(3+3*x+2*x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, Jun 13 2016: (Start)

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

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

%p seq(floor((8*n-6)/3), n=1..52); # _Gary Detlefs_, Mar 07 2010

%t f[n_] := 3 n - Floor[n/3]; Array[f, 52, 0] (* Or *)

%t Cases[ Range[0, 136], n_ /; MatchQ[ Mod[n, 8], 0 | 3 | 6]] (* _Robert G. Wilson v_, Jul 10 2011 *)

%o (Magma) [Floor((8*n-6)/3): n in [1..60]]; // _Vincenzo Librandi_, Jul 11 2011

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_