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A256659
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Rectangular array by antidiagonals: row n consists of numbers k such that -F(n+1) is the trace of the minimal alternating Fibonacci representation of k, where F = A000045 (Fibonacci numbers).
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2
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4, 7, 6, 12, 11, 10, 20, 19, 18, 16, 25, 32, 31, 29, 26, 33, 40, 52, 50, 47, 42, 38, 53, 65, 84, 81, 76, 68, 41, 61, 86, 105, 136, 131, 123, 110, 46, 66, 99, 139, 170, 220, 212, 199, 178, 54, 74, 107, 160, 225, 275, 356, 343, 322, 288, 59, 87, 120, 173, 259
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OFFSET
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1,1
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COMMENTS
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See A256655 for definitions. This array and the array at A256658 partition the positive integers. The row differences are Fibonacci numbers. The columns satisfy the Fibonacci recurrence x(n) = x(n-1) + x(n-2).
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LINKS
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EXAMPLE
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Northwest corner:
4 7 12 20 25 33 38 41 46
6 11 19 32 40 53 61 66 74
10 18 31 52 65 86 99 102 120
16 29 50 84 105 139 160 173 194
26 47 81 136 170 225 259 280 314
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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[18]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
t = Table[Last[r[n]], {n, 0, 1000}]; (* A256656 *)
TableForm[Table[Flatten[-1 + Position[t, b[n]]], {n, 2, 8}]] (* A256658 *)
TableForm[Table[Flatten[-1 + Position[t, -b[n]]], {n, 2, 8}]] (* A256659 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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