|
|
A366767
|
|
Array read by antidiagonals, where each row is the counting sequence of a certain type of fixed polyominoids.
|
|
25
|
|
|
1, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 0, 2, 2, 0, 1, 0, 2, 4, 2, 0, 1, 0, 2, 12, 6, 1, 0, 1, 0, 2, 38, 22, 0, 1, 0, 1, 0, 2, 126, 88, 0, 2, 1, 0, 1, 0, 2, 432, 372, 0, 6, 2, 1, 0, 1, 0, 2, 1520, 1628, 0, 19, 6, 4, 3, 0, 1, 0, 2, 5450, 7312, 0, 63, 19, 20, 0, 3
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
See A366766 (corresponding array for free polyominoids) for details.
|
|
LINKS
|
|
|
EXAMPLE
|
Array begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12
---+--------------------------------------------------------------------
1 | 1 0 0 0 0 0 0 0 0 0 0 0
2 | 1 1 1 1 1 1 1 1 1 1 1 1
3 | 2 0 0 0 0 0 0 0 0 0 0 0
4 | 2 2 2 2 2 2 2 2 2 2 2 2
5 | 2 4 12 38 126 432 1520 5450 19820 72892 270536 1011722
6 | 2 6 22 88 372 1628 7312 33466 155446 730534 3466170 16576874
7 | 1 0 0 0 0 0 0 0 0 0 0 0
8 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861
9 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861
10 | 1 4 20 110 638 3832 23592 147941 940982 6053180 39299408 257105146
11 | 3 0 0 0 0 0 0 0 0 0 0 0
12 | 3 3 3 3 3 3 3 3 3 3 3 3
|
|
CROSSREFS
|
The following table lists some sequences that are rows of the array, together with the corresponding values of D, d, and C (see A366766). Some sequences occur in more than one row. Notation used in the table:
X: Allowed connection.
-: Not allowed connection (but may occur "by accident" as long as it is not needed for connectedness).
.: Not applicable for (D,d) in this row.
!: d < D and all connections have h = 0, so these polyominoids live in d < D dimensions only.
*: Whether a connection of type (g,h) is allowed or not is independent of h.
| | | connections |
| | | g:112223 |
n | D | d | h:010120 | sequence
----+---+---+-------------+----------
34 | 3 | 3 | * X.X..- |
36 | 3 | 3 | * X.-..X |
37 | 3 | 3 | * -.X..X |
38 | 3 | 3 | * X.X..X |
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|