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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.
5
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
0,3
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
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
EXAMPLE
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.
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 *)
CROSSREFS
See A280026, A280027 for similar sequences based on a spiral.
Sequence in context: A196063 A205450 A215674 * A110545 A104798 A243238
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 24 2016
EXTENSIONS
More terms from Alec Jones, Dec 25 2016
STATUS
approved