A279211 Fill an array by antidiagonals upwards; in the n-th cell, enter the number of earlier cells that can be seen from that cell.

0, 1, 2, 2, 4, 4, 3, 5, 6, 6, 4, 6, 8, 8, 8, 5, 7, 9, 10, 10, 10, 6, 8, 10, 12, 12, 12, 12, 7, 9, 11, 13, 14, 14, 14, 14, 8, 10, 12, 14, 16, 16, 16, 16, 16, 9, 11, 13, 15, 17, 18, 18, 18, 18, 18, 10, 12, 14, 16, 18, 20, 20, 20, 20, 20, 20, 11, 13, 15, 17

Offset: 0

Author

N. J. A. Sloane, Dec 24 2016

Keywords

• nonn
• tabl

Comments

"That can be seen from" means "that are on the same row, column, diagonal, or antidiagonal as".

Inspired by A279967.

Since the sum of row and column index is constant for elements in an antidiagonal, the entries along an antidiagonal on and above the diagonal equal twice the number of the antidiagonal. - Hartmut F. W. Hoft, Jun 29 2020

Examples

			The array begins:
x\y| 0  1  2  3  4  5  6 ...
---+--------------------
  0| 0  2  4  6  8 10 12 ...
  1| 1  4  6  8 10 12 ...
  2| 2  5  8 10 12 ...
  3| 3  6  9 12 ...
  4| 4  7 10 13 ...
  5| 5  8 11 14 ...
  6| ...
...
For example, when we get to the antidiagonal that reads 4, 6, 8 ..., the reason for the 8 is that from that cell we can see two cells that have been filled in above it (containing 4 and 6), two cells to the northwest (0, 4), two cells to the west (2, 5), and two to the southwest (4, 6), which is 8 cells, so a(12) = 8.
		

Links

• Alec Jones, Table of n, a(n) for n = 0..5049

Crossrefs

Cf. A279966, A279967, A279212.

See A280026, A280027 for similar sequences based on a spiral.

Programs

Mathematica

countCells[i_, j_] := i + 2*j + Min[i, j]
a279211[m_] := Map[countCells[m - #, #]&, Range[0, m]]
Flatten[Map[a279211,Range[0,10]]]  (* antidiagonals 0..10 data - Hartmut F. W. Hoft, Jun 29 2020 *)

Formula

T(x,y) = x+3*y if x >= y; T(x,y) = 2*(x+y) if x <= y.

T(i, j) = i + 2*j + min(i, j). - Hartmut F. W. Hoft, Jun 29 2020

Extensions

More terms from Alec Jones, Dec 25 2016