|
%I #42 Nov 29 2022 06:00:05
%S 0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,
%T 4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,
%U 7,0,4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,4,1,0,1,4,0,7,7,0,4,1,0,1
%N a(n) = n^2 mod 9.
%C Also decimal expansion of 4692347/333333333. - _Enrique Pérez Herrero_, Nov 27 2022
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-9).
%F G.f.: ( -x*(1+x)*(x^6+3*x^5-3*x^4+10*x^3-3*x^2+3*x+1) ) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). (End)
%F a(n) = A010878(A000290(n)) = A010878(n^2). - _Enrique Pérez Herrero_, Nov 27 2022
%t Table[Mod[n^2,9],{n,0,200}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 21 2011 *)
%t PowerMod[Range[0,200],2,9] (* _Harvey P. Dale_, Jun 11 2011 *)
%o (PARI) a(n)=[0,1,4,0,7,7,0,4,1][n%9+1] \\ _Charles R Greathouse IV_, Jun 11 2011
%o (PARI) a(n)=n^2%9 \\ _Charles R Greathouse IV_, Jun 11 2011
%Y Cf. A000290, A010878, A053879, A070430, A070431.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 12 2002
|
