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A156748
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a(1) = a(2) = a(3) = a(4) = 0, then a(n) = abs(a(n-1) -a(n-2) +2*a(n-3) -a(n-4)) -a(n-3) -1.
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2
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0, 0, 0, 0, -1, 0, 0, 2, 2, -1, -2, -2, 4, 4, 3, 4, 0, -2, -2, 3, 2, 4, 6, 0, -5, -4, 4, 6, 4, 5, 2, -4, -6, 0, 7, 6, 4, 4, -2, -1, 0, 8, 8, 0, -1, -2, 8, 8, 4, 5, 0, 0, 0, 4, 3, 0, 0, -2, 4, 5, 4, 4, 0, -4, -5, 4, 4, 10, 14, 3, -6, -6, 4, 10, 5, 4, 4, -6, 2, 7, 16, 16, 4, -4, -9, 8, 8, 22, 30, 7, -10, -10, 8
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OFFSET
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1,8
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COMMENTS
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There are 6 accumulation points for the sequence {a(n)/n} namely: -0.2, 0, 0.2, 0.4, 0.6 and 0.8.
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LINKS
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MATHEMATICA
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a[n_]:= a[n]= If[n<5, 0, Abs[a[n-1] -a[n-2] +2*a[n-3] -a[n-4]] -a[n-3] -1];
nxt[{a_, b_, c_, d_}]:={b, c, d, Abs[d-c+2b-a]-b-1}; NestList[nxt, {0, 0, 0, 0}, 100][[All, 1]] (* Harvey P. Dale, Sep 01 2021 *)
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PROG
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(Sage)
@CachedFunction
def a(n): return 0 if (n<5) else abs(a(n-1) -a(n-2) +2*a(n-3) -a(n-4)) -a(n-3) -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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