A141425 Period 6: repeat [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, 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, 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, 5, 7, 8, 1, 2, 4
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
Programs
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Magma
&cat [[1, 2, 4, 5, 7, 8]^^30]; // Wesley Ivan Hurt, Jun 28 2016
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Maple
A141425:=n->[1, 2, 4, 5, 7, 8][(n mod 6)+1]: seq(A141425(n), n=0..100); # Wesley Ivan Hurt, Jun 28 2016
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Mathematica
Select[ If[Mod[ #, 3] != 0, Mod[ #, 9], 0] & /@ Range@ 157, # > 0 &] (* Robert G. Wilson v, Aug 18 2008 *) PadRight[{},120,{1,2,4,5,7,8}] (* Harvey P. Dale, May 13 2018 *)
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PARI
a(n)=(1+(n%2)+3*((n-1)%6))/2 \\ Jaume Oliver Lafont, Aug 30 2009
Formula
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
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
From Wesley Ivan Hurt, Apr 20 2015: (Start)
Recurrence: a(n) = a(n-6) for n>6.
a(n) = (2+3*(5-n mod 3))*(n-1 mod 2)+(1+3*(1-n mod 3))*(n mod 2). (End)
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