A347065 Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = (1+sqrt(5))/2, h >= 1, 0 <= m <= n}.

1, 3, 1, 4, 3, 1, 6, 5, 3, 1, 8, 7, 5, 3, 1, 9, 9, 7, 5, 3, 1, 11, 11, 10, 7, 5, 3, 1, 12, 13, 12, 10, 7, 5, 3, 1, 14, 15, 14, 12, 10, 7, 5, 3, 1, 16, 17, 16, 15, 12, 10, 7, 5, 3, 1, 17, 19, 19, 17, 15, 12, 10, 7, 5, 3, 1, 19, 21, 21, 20, 17, 15, 12, 10, 7

Offset

1,2

Links

Table of n, a(n) for n=1..75.

Example

Corner:
   1 3 4 6  8  9 11 12 14 16 17 19 21
   1 3 5 7  9 11 13 15 17 19 21 23 25
   1 3 5 7 10 12 14 16 19 21 23 25 28
   1 3 5 7 10 12 15 17 20 22 24 26 29
   1 3 5 7 10 12 15 17 20 22 24 27 30
   1 3 5 7 10 12 15 17 20 22 24 27 30
   1 3 5 7 10 12 15 17 20 22 24 27 30

Mathematica

z = 100; 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}]] (* A347065, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347065, sequence *)

Crossrefs

Cf. A000201 (row 1), A005408 (row 2), A190511 (row 3), A020959 (limiting row).

Cf. A347066, A347067, A347068, A347069.

Sequence in context: A008314 A104568 A030758 * A322103 A272172 A104764

Adjacent sequences: A347062 A347063 A347064 * A347066 A347067 A347068

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 16 2021

Status

approved