|
| |
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
"That can be seen from" means "that are on the same row, column, diagonal, or antidiagonal as".
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
|
|
|
LINKS
|
|
|
|
FORMULA
|
T(x,y) = x+3*y if x >= y; T(x,y) = 2*(x+y) if x <= y.
|
|
|
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
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
