cp's OEIS Frontend

A141425 Period 6: repeat [1, 2, 4, 5, 7, 8].

%I A141425 #45 Aug 04 2025 09:01:18
%S A141425 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 A141425 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 A141425 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 A141425 Period 6: repeat [1, 2, 4, 5, 7, 8].
%H A141425 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F A141425 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 A141425 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 A141425 From _Wesley Ivan Hurt_, Apr 20 2015: (Start)
%F A141425 Recurrence: a(n) = a(n-6) for n>6.
%F A141425 a(n) = (2+3*(5-n mod 3))*(n-1 mod 2)+(1+3*(1-n mod 3))*(n mod 2). (End)
%F A141425 E.g.f.: 3*cos(sqrt(3)*x/2)*cosh(x/2) + 5*cosh(x) - sqrt(3)*sin(sqrt(3)*x/2)*(2*cosh(x/2) + sinh(x/2)) + 4*sinh(x) - 8. - _Stefano Spezia_, Aug 04 2025
%p A141425 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 A141425 Select[ If[Mod[ #, 3] != 0, Mod[ #, 9], 0] & /@ Range@ 157, # > 0 &] (* _Robert G. Wilson v_, Aug 18 2008 *)
%t A141425 PadRight[{},120,{1,2,4,5,7,8}] (* _Harvey P. Dale_, May 13 2018 *)
%o A141425 (PARI) a(n)=(1+(n%2)+3*((n-1)%6))/2 \\ _Jaume Oliver Lafont_, Aug 30 2009
%o A141425 (Magma) &cat [[1, 2, 4, 5, 7, 8]^^30]; // _Wesley Ivan Hurt_, Jun 28 2016
%K A141425 nonn,easy
%O A141425 1,2
%A A141425 _Paul Curtz_, Aug 06 2008