A366767 Array read by antidiagonals, where each row is the counting sequence of a certain type of fixed polyominoids.
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
Offset: 1
Examples
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
Links
- Pontus von Brömssen, Python programs that relate row numbers and parameter sets.
- Wikipedia, Polyominoid.
- Index entries for sequences related to polyominoes.
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
----+---+---+-------------+----------
1 | 1 | 1 | * -..... | A063524
2 | 1 | 1 | * X..... | A000012
3 |!2 | 1 | * --.... | 2*A063524
4 |!2 | 1 | X-.... | 2*A000012
5 | 2 | 1 | -X.... | 2*A001168
6 | 2 | 1 | * XX.... | A096267
7 | 2 | 2 | * -.-... | A063524
8 | 2 | 2 | * X.-... | A001168
9 | 2 | 2 | * -.X... | A001168
10 | 2 | 2 | * X.X... | A006770
11 |!3 | 1 | * --.... | 3*A063524
12 |!3 | 1 | X-.... | 3*A000012
13 | 3 | 1 | -X.... | A365655
14 | 3 | 1 | * XX.... | A365560
15 |!3 | 2 | * ----.. | 3*A063524
16 |!3 | 2 | X---.. | 3*A001168
17 | 3 | 2 | -X--.. | A365655
18 | 3 | 2 | * XX--.. | A075678
19 |!3 | 2 | --X-.. | 3*A001168
20 |!3 | 2 | X-X-.. | 3*A006770
21 | 3 | 2 | -XX-.. | A365996
22 | 3 | 2 | XXX-.. | A365998
23 | 3 | 2 | ---X.. | A366000
24 | 3 | 2 | X--X.. | A366002
25 | 3 | 2 | -X-X.. | A366004
26 | 3 | 2 | XX-X.. | A366006
27 | 3 | 2 | * --XX.. | A365653
28 | 3 | 2 | X-XX.. | A366008
29 | 3 | 2 | -XXX.. | A366010
30 | 3 | 2 | * XXXX.. | A365651
31 | 3 | 3 | * -.-..- | A063524
32 | 3 | 3 | * X.-..- | A001931
33 | 3 | 3 | * -.X..- | A039742
34 | 3 | 3 | * X.X..- |
35 | 3 | 3 | * -.-..X | A039741
36 | 3 | 3 | * X.-..X |
37 | 3 | 3 | * -.X..X |
38 | 3 | 3 | * X.X..X |
39 |!4 | 1 | * --.... | 4*A063524
40 |!4 | 1 | X-.... | 4*A000012
41 | 4 | 1 | -X.... | A366341
42 | 4 | 1 | * XX.... | A365562
43 |!4 | 2 | * -----. | 6*A063524
44 |!4 | 2 | X----. | 6*A001168
45 | 4 | 2 | -X---. | A366339
46 | 4 | 2 | * XX---. | A366335
47 |!4 | 2 | --X--. | 6*A001168
48 |!4 | 2 | X-X--. | 6*A006770
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