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A138189
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Sequence built on pattern (1,-even,-even) beginning 1,-2,-2.
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2
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1, -2, -2, 1, -4, -4, 1, -6, -6, 1, -8, -8, 1, -10, -10, 1, -12, -12, 1, -14, -14, 1, -16, -16, 1, -18, -18, 1, -20, -20, 1, -22, -22, 1, -24, -24, 1, -26, -26, 1, -28, -28, 1, -30, -30, 1, -32, -32, 1, -34, -34, 1, -36, -36, 1, -38, -38, 1, -40, -40
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 -2*x -2*x^2 -x^3)/(1 -2*x^3 +x^6).
a(n) = -b(n+3), where b(n) = abs(2*b(n-1) - b(n-2)) - b(n-1) - 1 and b(1) = b(2) = 0.
a(n) = 1 if (n mod 3) = 0, -2*(floor(n/3) + 1) if (n mod 3) = 1 or (n mod 3) = 2. (End)
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MATHEMATICA
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Join[{1}, Riffle[Flatten[{-2#, -2#}&/@Range[25]], 1, 3]] (* Harvey P. Dale, Nov 02 2011 *)
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PROG
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(Magma)
b:= [n le 2 select 0 else Abs(2*Self(n-1) -Self(n-2)) -Self(n-1)-1: n in [1..120]];
(Sage)
@CachedFunction
if (n%3==0): return 1
elif (n%3==1): return -2*(n//3 +1)
else: return -2*(n//3 +1)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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