A347067 Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = 1/sqrt(2), h >= 1, 0 <= m <= n}.

2, 4, 4, 7, 8, 6, 9, 13, 13, 10, 12, 17, 21, 21, 15, 14, 21, 28, 33, 32, 19, 16, 22, 34, 44, 49, 40, 25, 19, 26, 35, 54, 66, 61, 51, 41, 21, 30, 41, 55, 82, 82, 78, 83, 63, 24, 35, 48, 65, 83, 102, 105, 126, 128, 95, 26, 38, 56, 76, 98, 103, 130, 169, 193

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Example

Corner:
   2,  4,   7,   9,  12,  14,  16,  19,  21, ...
   4,  8,  13,  17,  21,  22,  26,  30,  35, ...
   6, 13,  21,  28,  34,  35,  41,  48,  56, ...
  10, 21,  33,  44,  54,  55,  65,  76,  88, ...
  15, 32,  49,  66,  82,  83,  98, 115, 133, ...
  19, 40,  61,  82, 102, 103, 122, 143, 165, ...
  25, 51,  78, 105, 130, 131, 156, 183, 210, ...
  41, 83, 126, 169, 210, 211, 252, 283, 310, ...
  ...

Mathematica

z = 100; r = N[1/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}]] (* A347067, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347067, sequence *)

Crossrefs

Cf. A003151 (row 1), A347065, A347066, A347068, A347069.

Sequence in context: A286014 A102465 A139825 * A164721 A194118 A266188

Adjacent sequences: A347064 A347065 A347066 * A347068 A347069 A347070

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 02 2021

Status

approved