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A111951
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Period 8: repeat [0,3,1,2,2,1,3,0].
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1
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0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 3, 1, 2, 2, 1, 3, 0
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OFFSET
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0,2
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COMMENTS
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Permutation of {0,1,2,3} followed by its reversal, repeated.
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LINKS
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FORMULA
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G.f.: (3x + x^2 + 2x^3 + 2x^4 + x^5 + 3x^6)/(1 - x^8);
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7);
a(n) = n(7n-1)/2 mod 4 = A022264(n) mod 4.
G.f.: -x*(3 - 2*x + 4*x^2 - 2*x^3 + 3*x^4) / ( (x-1)*(1+x^2)*(1+x^4) ). - R. J. Mathar, Feb 20 2015
a(n) = (3 + r/2 - s/2 + 2*cos(Pi*(1+2*n-r-s+t)/8) - 2*cos(Pi*(1-2*n+r-s+t)/8) - 2*sin(Pi*(1-2*n-r+s+t)/8))/2 where r = 2*sin(n*Pi/2), s = 2*cos(n*Pi/2) and t = cos(n*Pi). - Wesley Ivan Hurt, Oct 05 2018
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Name changed, the original name moved to comments. - Antti Karttunen, Aug 10 2017
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STATUS
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approved
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