A256658 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).

1, 9, 2, 14, 15, 3, 17, 23, 24, 5, 22, 28, 37, 39, 8, 27, 36, 45, 60, 63, 13, 30, 44, 58, 73, 97, 102, 21, 35, 49, 71, 94, 118, 157, 165, 34, 43, 57, 79, 115, 152, 191, 254, 267, 55, 48, 70, 92, 128, 186, 246, 309, 411, 432, 89, 51, 78, 113, 149, 207, 301

Offset

1,2

Comments

See A256655 for definitions. This array and the array at A256659 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..61.

Example

Northwest corner:
1    9     14    17    22    27    30    35    43
2    15    23    28    36    44    49    57    70
3    24    37    45    58    71    79    92    113
5    39    69    73    94    115   128   149   183
8    63    97    118   152   186   207   241   296
13   102   157   191   246   301   335   390   479

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, A256659.

Sequence in context: A266565 A090298 A248315 * A094581 A040080 A272033

Adjacent sequences: A256655 A256656 A256657 * A256659 A256660 A256661

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Apr 08 2015

Status

approved