A152467 - OEIS

%I #42 Nov 13 2022 08:36:29

%S 0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,

%T 5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,

%U 10,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14

%N a(n) = floor(n/6).

%C Apart from initial terms, same as A097992. - _Philippe Deléham_, Dec 06 2008

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).

%F From _R. J. Mathar_ and _Philippe Deléham_, Dec 06 2008: (Start)

%F a(n) = floor(n/6) = a(n-6) + 1.

%F G.f.: x^6/((1-x)^2*(1+x)*(1+x+x^2)*(x^2-x+1)). (End)

%F a(n) = (6*n - 15 + 3*(-1)^n + 12*sin( (2*n+1)*Pi/6 ) + 4*sqrt(3)*sin( (2n+1)*Pi/3) )/36.

%F a(n) = floor( (3*n-2)/2 - (4*n-3)/3 ). - _Robert G. Wilson v_, Jun 04 2011

%F E.g.f.: (6*cos(sqrt(3)*x/2)*cosh(x/2) + 3*(x - 2)*cosh(x) + 2*sqrt(3)*sin(sqrt(3)*x/2)*(2*cosh(x/2) + sinh(x/2)) + 3*(x - 3)*sinh(x))/18. - _Stefano Spezia_, Nov 13 2022

%p A152467:=n->floor(n/6); seq(A152467(n), n=0..100); # _Wesley Ivan Hurt_, Dec 10 2013

%t Table[Floor[n/6], {n, 0, 100}] (* _Wesley Ivan Hurt_, Dec 10 2013 *)

%o (Sage) [floor(n/6) for n in range(0,90)] # _Zerinvary Lajos_, Dec 02 2009

%o (PARI) a(n)=n\6 \\ _Charles R Greathouse IV_, Jun 04 2011

%Y Cf. A097992.

%K nonn,easy

%O 0,13

%A _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008