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).

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).

Links

Table of n, a(n) for n=1..60.

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

Cf. A000045, A256655, A246658.

Sequence in context: A354763 A255248 A122460 * A063845 A188730 A019714

Adjacent sequences: A256656 A256657 A256658 * A256660 A256661 A256662

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Apr 08 2015

Status

approved