A256661 Rectangular array by antidiagonals: row n shows the numbers k such that R(k) consists of n terms, where R(k) is the minimal alternating Fibonacci representation of k.

1, 2, 4, 3, 6, 9, 5, 7, 14, 25, 8, 10, 15, 38, 64, 13, 11, 17, 40, 98, 169, 21, 12, 22, 41, 103, 258, 441, 34, 16, 23, 46, 104, 271, 674, 1156, 55, 18, 24, 59, 106, 273, 708, 1766, 3025, 89, 19, 27, 61, 119, 274, 713, 1855, 4622, 7921, 144, 20, 28, 62, 153

Offset

1,2

Comments

See A256655 for definitions. Every positive integer occurs exactly once.

(row 1): A000045 (Fibonacci numbers)

(col 1): A007598 (squared Fibonacci numbers)

(col 2): A127546 (conjectured)

Links

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

Example

Northwest corner:
1     2     3     5     8     13    21
4     6     7     10    11    12    62
9     14    15    17    22    23    24
25    38    40    41    46    59    61
64    98    103   104   106   119   153
169   258   271   273   274   279   313
R(1) = 1, in row 1
R(2) = 2, in row 1
R(3) = 3, in row 1
R(4) = 5 - 1, in row 2
R(9) = 13 - 5 + 1, in row 3
R(25) = 34 - 13 + 5 - 1, in row 4
R(64) = 89 - 34 + 13 - 5 + 1, in row 5

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[23];  r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
u = Table[Length[r[n]], {n, 1, 6000}];
TableForm[Table[Flatten[Position[u, k]], {k, 1, 9}]]

Crossrefs

Cf. A000045, A256655, A007598, A127546.

Sequence in context: A143516 A120620 A094608 * A370923 A179216 A192176

Adjacent sequences: A256658 A256659 A256660 * A256662 A256663 A256664

Keyword

nonn,easy,tabl

Author

Clark Kimberling, Apr 08 2015

Status

approved