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A156747
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a(1) = a(2) = a(3) = 0, then a(n) = abs(a(n-1) + 2*a(n-2) - a(n-3)) - a(n-2) - 1.
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1
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0, 0, 0, -1, 0, 2, 2, 3, 2, 2, 0, -1, 2, 0, 2, -1, 0, 4, 4, 7, 6, 8, 6, 7, 4, 4, 0, -1, 4, 2, 6, 3, 6, 2, 4, -1, 0, 6, 6, 11, 10, 14, 12, 15, 12, 14, 10, 11, 6, 6, 0, -1, 6, 4, 10, 7, 12, 8, 12, 7, 10, 4, 6, -1, 0, 8, 8, 15, 14, 20, 18, 23, 20, 24, 20, 23, 18, 20, 14, 15, 8, 8, 0, -1, 8, 6, 14, 11
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OFFSET
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1,6
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COMMENTS
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A jumping flea sequence of order 3 (take a look at the graph and see A104156 for a sequence of order 2).
For n>=1, a(n^2 + (3/2)*(1 - (-1)^n)) = -1; for n>=5, a(n^2 - 2 + (1+(-1)^n)/2) = 0; between zeros there are simple patterns.
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LINKS
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MATHEMATICA
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RecurrenceTable[{a[1]==a[2]==a[3]==0, a[n]==Abs[a[n-1]+2a[n-2]-a[n-3]]-a[n-2]-1}, a, {n, 90}] (* Harvey P. Dale, Aug 19 2019 *)
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PROG
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(Magma)
a:= func< n | n lt 4 select 0 else Abs(Self(n-1) +2*Self(n-2) -Self(n-3)) -Self(n-2) -1 >;
(Sage)
@CachedFunction
def a(n): return 0 if (n<4) else abs(a(n-1) +2*a(n-2) -a(n-3)) -a(n-2) -1
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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