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A100285
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Expansion of (1+5*x^2)/(1-x+x^2-x^3).
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3
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1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1
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OFFSET
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0,3
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COMMENTS
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This sequence is periodic. - T. D. Noe, Nov 09 2006
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LINKS
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FORMULA
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a(n) = a(n-1) - a(n-2) + a(n-3)
a(n) = 3 - 2*cos(Pi*n/2) - 2*sin(Pi*n/2).
a(n) = ((n+2 mod 4) + 5*(n mod 4) - 6*(n mod 2))/2.
a(n) = 3 -((1+i)*(-1)^n +(1-i)*i^n) = 3 -2*(A056594(n) +A056594(n-1)).
G.f.: (1+5*x^2)/((1-x)*(1+x^2)).
E.g.f.: 3*exp(x) - 2*cos(x) - 2*sin(x). (End)
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MATHEMATICA
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CoefficientList[Series[(1+5x^2)/(1-x+x^2-x^3), {x, 0, 100}], x] (* or *) PadRight[{}, 100, {1, 1, 5, 5}] (* Harvey P. Dale, Jun 02 2021 *)
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PROG
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(Magma) [(((n+2) mod 4) + 5*(n mod 4) - 6*(n mod 2))/2: n in [0..100]]; // G. C. Greubel, Feb 06 2023
(SageMath)
def A100285(n): return (((n+2)%4) +5*(n%4) -6*(n%2))/2
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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