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A255973
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Trace of the minimal alternating Fibonacci representation of n.
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2
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0, 1, 2, 3, -1, 5, -2, -1, 8, 1, -3, -2, -1, 13, 1, 2, -5, 1, -3, -2, -1, 21, 1, 2, 3, -1, -8, 1, 2, -5, 1, -3, -2, -1, 34, 1, 2, 3, -1, 5, -2, -1, -13, 1, 2, 3, -1, -8, 1, 2, -5, 1, -3, -2, -1, 55, 1, 2, 3, -1, 5, -2, -1, 8, 1, -3, -2, -1, -21, 1, 2, 3, -1
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OFFSET
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0,3
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COMMENTS
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LINKS
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EXAMPLE
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Let R(k) be the minimal alternating Fibonacci representation of k. The trace of R(k) is the last term.
R(1) = 1, trace = 1
R(2) = 2, trace = 2
R(3) = 3, trace = 3
R(4) = 5 - 1, trace = -1
R(5) = 5, trace = 5
R(6) = 6 - 2, trace = -2
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MATHEMATICA
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b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
g = h[12]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[Last[r[n]], {n, 0, 200}] (* A255973 *)
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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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