A347066 Rectangular array (T(n,k)), by antidiagonals: T(n,k) is the position of k in the ordering of {h/r^m, r = sqrt(2), h >= 1, 0 <= m <= n}.

1, 3, 1, 5, 3, 1, 6, 6, 3, 1, 8, 7, 7, 3, 1, 10, 10, 8, 7, 3, 1, 11, 12, 11, 8, 7, 3, 1, 13, 14, 14, 12, 8, 7, 3, 1, 15, 16, 16, 15, 12, 8, 7, 3, 1, 17, 19, 18, 17, 16, 12, 8, 7, 3, 1, 18, 21, 21, 19, 18, 16, 12, 8, 7, 3, 1, 20, 23, 23, 23, 20, 18, 16, 12, 8

Offset

1,2

Links

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

Example

Corner:
  1, 3, 5, 6,  8, 10, 11, 13, 15, 17, 18, 20, ...
  1, 3, 6, 7, 10, 12, 14, 16, 19, 21, 23, 25, ...
  1, 3, 7, 8, 11, 14, 16, 18, 21, 23, 25, 28, ...
  1, 3, 7, 8, 12, 15, 17, 19, 23, 25, 27, 30, ...
  1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
  1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
  1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
  ...

Mathematica

z = 100; r = N[Sqrt[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}]] (* A347066, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347066, sequence *)

Crossrefs

Cf. A003152 (row 1), A347065, A347067, A347068, A347069.

Sequence in context: A147754 A360325 A084305 * A099375 A348835 A130301

Adjacent sequences: A347063 A347064 A347065 * A347067 A347068 A347069

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 02 2021

Status

approved