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A256659
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).
2
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
OFFSET
1,1
COMMENTS
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).
EXAMPLE
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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Apr 08 2015
STATUS
approved