login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(4n) = a(4n+1) = a(4n+2) = A001477(n), a(4n+3) = A005408(n).
4

%I #19 May 06 2021 12:14:53

%S 0,0,0,1,1,1,1,3,2,2,2,5,3,3,3,7,4,4,4,9,5,5,5,11,6,6,6,13,7,7,7,15,8,

%T 8,8,17,9,9,9,19,10,10,10,21,11,11,11,23,12,12,12,25,13,13,13,27,14,

%U 14,14,29,15,15,15,31,16,16,16,33,17,17,17

%N a(4n) = a(4n+1) = a(4n+2) = A001477(n), a(4n+3) = A005408(n).

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).

%F O.g.f.: x^3*(1+x+x^2+x^3+x^4)/((1-x)^2*(1+x)^2*(1+x^2)^2). - _R. J. Mathar_, Aug 22 2008

%F a(0)=0, a(1)=0, a(2)=0, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=3, a(n)=2*a(n-4)- a(n-8). - _Harvey P. Dale_, Mar 04 2012

%F a(n) = cos(n*Pi/2)/4-(n-1)*(2*sin(n*Pi/2)+(-1)^n-5)/16. - _Wesley Ivan Hurt_, May 05 2021

%t CoefficientList[Series[x^3(1+x+x^2+x^3+x^4)/((1-x)^2(1+x)^2(1+x^2)^2),{x,0,80}],x] (* or *) LinearRecurrence[{0,0,0,2,0,0,0,-1},{0,0,0,1,1,1,1,3},80] (* _Harvey P. Dale_, Mar 04 2012 *)

%K nonn

%O 0,8

%A _Paul Curtz_, Jul 20 2007

%E Edited by _N. J. A. Sloane_, Sep 28 2007