%I #41 Mar 15 2024 02:19:28

%S 1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,

%T 7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,

%U 4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4,5,7,8,1,2,4

%N Period 6: repeat [1, 2, 4, 5, 7, 8].

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F G.f.: x*(1+2*x+4*x^2+5*x^3+7*x^4+8*x^5)/((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)). [_R. J. Mathar_, Nov 11 2008]

%F a(n) = 9/2 - 3*cos(Pi*(n-1)/3)/2 - 3^(3/2)*sin(Pi*(n-1)/3)/2 - 3*cos(2*Pi*(n-1)/3)/2 - 3^(1/2)*sin(2*Pi*(n-1)/3)/2 + (-1)^n/2. - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, Apr 20 2015: (Start)

%F Recurrence: a(n) = a(n-6) for n>6.

%F a(n) = (2+3*(5-n mod 3))*(n-1 mod 2)+(1+3*(1-n mod 3))*(n mod 2). (End)

%p A141425:=n->[1, 2, 4, 5, 7, 8][(n mod 6)+1]: seq(A141425(n), n=0..100); # _Wesley Ivan Hurt_, Jun 28 2016

%t Select[ If[Mod[ #, 3] != 0, Mod[ #, 9], 0] & /@ Range@ 157, # > 0 &] (* _Robert G. Wilson v_, Aug 18 2008 *)

%t PadRight[{},120,{1,2,4,5,7,8}] (* _Harvey P. Dale_, May 13 2018 *)

%o (PARI) a(n)=(1+(n%2)+3*((n-1)%6))/2 \\ _Jaume Oliver Lafont_, Aug 30 2009

%o (Magma) &cat [[1, 2, 4, 5, 7, 8]^^30]; // _Wesley Ivan Hurt_, Jun 28 2016

%K nonn,easy

%O 1,2

%A _Paul Curtz_, Aug 06 2008