A347068 Rectangular array (T(n,k)), by downward antidiagonals: T(n,k) = position of k in the ordering of {h*r^m, r = 1/(golden ratio), h >= 1, 0 <= m <= n}.

2, 5, 4, 7, 10, 8, 10, 14, 18, 14, 13, 20, 26, 31, 25, 15, 26, 36, 46, 53, 42, 18, 30, 47, 63, 79, 88, 71, 20, 36, 55, 81, 107, 132, 146, 117, 23, 40, 65, 96, 136, 178, 219, 239, 193, 26, 46, 73, 112, 162, 225, 294, 359, 391, 315, 28, 52, 84, 127, 189, 269

Offset

1,1

Comments

Row 1: A001950 (upper Wythoff sequence);

row 2: A283234;

row 3: A190508;

col 1: A020956.

Links

Table of n, a(n) for n=1..61.

Example

Corner:
    2,   5,   7,  10,  13,  15,  18,  20,  23, ...
    4,  10,  14,  20,  26,  30,  36,  40,  46, ...
    8,  18,  26,  36,  47,  55,  65,  73,  84, ...
   14,  31,  46,  63,  81,  96, 112, 127, 145, ...
   25,  53,  79, 107, 136, 162, 189, 215, 244, ...
   42,  88, 132, 178, 225, 269, 314, 358, 405, ...
   71, 146, 219, 294, 370, 443, 517, 590, 666, ...
   ...

Mathematica

z = 1000; r = N[(-1+Sqrt[5])/2];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347068, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347068, sequence *)

Crossrefs

Cf. A001950, A020956, A283234, A190508, A347065, A347066, A347067, A347069.

Sequence in context: A153990 A154811 A309513 * A296203 A036237 A015948

Adjacent sequences: A347065 A347066 A347067 * A347069 A347070 A347071

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 02 2021

Status

approved