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A216178
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Period 4: repeat [4, 1, 0, -3].
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1
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4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4).
G.f.: (4+x-3*x^3) / ((1-x)*(1+x)*(1+x^2)). - R. J. Mathar, Mar 10 2013
a(n) = 1/2+3*I^(2*n)/2+(1+I)*I^(-n)+(1-I)*I^n.
a(n) = (1+3*cos(n*Pi)+4*cos(n*Pi/2)+4*sin(n*Pi/2)+3*I*sin(n*Pi))/2. (End)
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MAPLE
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MATHEMATICA
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PadRight[{}, 100, {4, 1, 0, -3}] (* or *) LinearRecurrence[{0, 0, 0, 1}, {4, 1, 0, -3}, 100] (* Harvey P. Dale, Nov 28 2014 *)
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PROG
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(Magma) for n in [0 .. 50] do (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4); end for;
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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