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A088689
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Jacobsthal numbers modulo 3.
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4
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0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1
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OFFSET
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0,5
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COMMENTS
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Period 6 = A175286(3).
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LINKS
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Table of n, a(n) for n=0..104.
M. E. Muldoon and A. A. Ungar, Beyond Sin and Cos, Mathematics Magazine, 69,1,(1996).
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1).
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FORMULA
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E.g.f.: exp(x) - exp(-x/2)*cos(sqrt(3)*x/2) - 3*exp(x/2)*sin(sqrt(3)*x/2)/sqrt(3);
E.g.f.: F(1, 3, 1, x) + F(1, 3, 2, x) + F(1, 6, 4, x) + F(1, 6, 5, x);
a(n) = a(n-6), with a(0)=0, a(1)=a(2)=1, a(3)=0, a(4)=a(5)=2;
a(n) = 1 - cos(2*Pi*n/3) - 3*sin(Pi*n/3)/3.
a(n) = A001045(n) mod 3.
G.f.: x*(1+2*x^3)/(1-x+x^2-x^3+x^4-x^5); a(n)=a(n-1)-a(n-2)+a(n-3)-a(n-4)+a(n-5). - Paul Barry, Jul 27 2005
a(n) = 1/30*{12*(n mod 6)+2*[(n+1) mod 6]-8*[(n+2) mod 6]+7*[(n+3) mod 6]+2*[(n+4) mod 6]-3*[(n+5) mod 6]} with n>=0. - Paolo P. Lava, Nov 27 2006
a(n) = ( n * floor( 3(n+1)/2 ) - 2n ) mod 3. - Wesley Ivan Hurt, Oct 13 2013
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MAPLE
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A088689:=n->(n*floor(3*(n+1)/2) - 2*n) mod 3; seq(A088689(k), k=0..70); # Wesley Ivan Hurt, Oct 13 2013
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MATHEMATICA
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Table[Mod[n*Floor[3(n+1)/2] - 2n, 3], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 13 2013 *)
LinearRecurrence[{1, -1, 1, -1, 1}, {0, 1, 1, 0, 2}, 120] (* Harvey P. Dale, Apr 09 2020 *)
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PROG
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(PARI) a(n)=[0, 1, 1, 0, 2, 2][n%6+1] \\ Charles R Greathouse IV, Oct 16 2015
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CROSSREFS
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Sequence in context: A124210 A287447 A110568 * A076898 A174294 A089385
Adjacent sequences: A088686 A088687 A088688 * A088690 A088691 A088692
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Oct 06 2003
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STATUS
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approved
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