A335607 Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = sqrt(2).

0, 1, 1, 2, 2, 2, 4, 3, 3, 3, 5, 5, 4, 4, 4, 7, 6, 6, 5, 5, 5, 8, 8, 7, 7, 6, 6, 6, 9, 9, 9, 8, 8, 7, 7, 7, 11, 10, 10, 10, 9, 9, 8, 8, 8, 12, 12, 11, 11, 11, 10, 10, 9, 9, 9, 14, 13, 13, 12, 12, 12, 11, 11, 10, 10, 10, 15, 15, 14, 14, 13, 13, 13, 12, 12, 11

Offset

0,4

Comments

Column 0: Nonnegative integers.

Row 0: A001951 (Beatty sequence of sqrt(2)).

Main diagonal: (0,2,4,7,...): A003151 with 0 prepended.

Links

Table of n, a(n) for n=0..75.

Formula

T(n,k) = floor(n + k*r), where r = sqrt(2).

Example

Northwest corner:
  0   1   2   4    5    7    8    9   11
  1   2   3   5    6    8    9   10   12
  2   3   4   6    7    9   10   11   13
  3   4   5   7    8   10   11   12   14
  4   5   6   8    9   11   12   13   15
  5   6   7   9   10   12   13   14   16

Mathematica

t[n_, k_] := Floor[n + k*Sqrt[2]];
Grid[Table[t[n, k], {n, 0, 10}, {k, 0, 10}]]   (* A335607 array *)
u = Table[t[n - k, k], {n, 0, 13}, {k, n, 0, -1}] // Flatten  (* A335607 seq *)

Crossrefs

Cf. A001951, A003151, A002193.

Sequence in context: A257126 A050493 A331851 * A366192 A347628 A338796

Adjacent sequences: A335604 A335605 A335606 * A335608 A335609 A335610

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Jun 15 2020

Status

approved