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A168330
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Period 2: repeat [3, -2].
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1
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3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2, 3, -2
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OFFSET
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1,1
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COMMENTS
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Binomial transform of 3 followed by a signed version of A020714.
Inverse binomial transform of 3 followed by A000079.
A084964 without first two terms gives partial sums.
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LINKS
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FORMULA
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a(n) = (-5*(-1)^n + 1)/2.
a(n+1) - a(n) = 5*(-1)^n.
a(n) = -a(n-1) + 1 for n > 1; a(1) = 3.
a(n) = a(n-2) for n > 2; a(1) = 3, a(2) = -2.
G.f.: x*(3 - 2*x)/((1-x)*(1+x)).
E.g.f.: (1/2)*(1 - exp(-x))*(5 + exp(x)). - G. C. Greubel, Jul 18 2016
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MATHEMATICA
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LinearRecurrence[{0, 1}, {3, -2}, 25] (* G. C. Greubel, Jul 18 2016 *)
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PROG
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(Magma) &cat[[3, -2]: n in [1..42]];
(Magma) [n eq 1 select 3 else -Self(n-1)+1:n in [1..84]];
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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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