This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A366767 #9 Oct 30 2023 11:20:05 %S A366767 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, %T A366767 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, %U A366767 1628,0,19,6,4,3,0,1,0,2,5450,7312,0,63,19,20,0,3 %N A366767 Array read by antidiagonals, where each row is the counting sequence of a certain type of fixed polyominoids. %C A366767 See A366766 (corresponding array for free polyominoids) for details. %H A366767 Pontus von Brömssen, <a href="https://oeis.org/A366766/a366766.py.txt">Python programs that relate row numbers and parameter sets</a>. %H A366767 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyominoid">Polyominoid</a>. %H A366767 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %e A366767 Array begins: %e A366767 n\k| 1 2 3 4 5 6 7 8 9 10 11 12 %e A366767 ---+-------------------------------------------------------------------- %e A366767 1 | 1 0 0 0 0 0 0 0 0 0 0 0 %e A366767 2 | 1 1 1 1 1 1 1 1 1 1 1 1 %e A366767 3 | 2 0 0 0 0 0 0 0 0 0 0 0 %e A366767 4 | 2 2 2 2 2 2 2 2 2 2 2 2 %e A366767 5 | 2 4 12 38 126 432 1520 5450 19820 72892 270536 1011722 %e A366767 6 | 2 6 22 88 372 1628 7312 33466 155446 730534 3466170 16576874 %e A366767 7 | 1 0 0 0 0 0 0 0 0 0 0 0 %e A366767 8 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861 %e A366767 9 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861 %e A366767 10 | 1 4 20 110 638 3832 23592 147941 940982 6053180 39299408 257105146 %e A366767 11 | 3 0 0 0 0 0 0 0 0 0 0 0 %e A366767 12 | 3 3 3 3 3 3 3 3 3 3 3 3 %Y A366767 Cf. A366766 (free), A366768. %Y A366767 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: %Y A366767 X: Allowed connection. %Y A366767 -: Not allowed connection (but may occur "by accident" as long as it is not needed for connectedness). %Y A366767 .: Not applicable for (D,d) in this row. %Y A366767 !: d < D and all connections have h = 0, so these polyominoids live in d < D dimensions only. %Y A366767 *: Whether a connection of type (g,h) is allowed or not is independent of h. %Y A366767 | | | connections | %Y A366767 | | | g:112223 | %Y A366767 n | D | d | h:010120 | sequence %Y A366767 ----+---+---+-------------+---------- %Y A366767 1 | 1 | 1 | * -..... | A063524 %Y A366767 2 | 1 | 1 | * X..... | A000012 %Y A366767 3 |!2 | 1 | * --.... | 2*A063524 %Y A366767 4 |!2 | 1 | X-.... | 2*A000012 %Y A366767 5 | 2 | 1 | -X.... | 2*A001168 %Y A366767 6 | 2 | 1 | * XX.... | A096267 %Y A366767 7 | 2 | 2 | * -.-... | A063524 %Y A366767 8 | 2 | 2 | * X.-... | A001168 %Y A366767 9 | 2 | 2 | * -.X... | A001168 %Y A366767 10 | 2 | 2 | * X.X... | A006770 %Y A366767 11 |!3 | 1 | * --.... | 3*A063524 %Y A366767 12 |!3 | 1 | X-.... | 3*A000012 %Y A366767 13 | 3 | 1 | -X.... | A365655 %Y A366767 14 | 3 | 1 | * XX.... | A365560 %Y A366767 15 |!3 | 2 | * ----.. | 3*A063524 %Y A366767 16 |!3 | 2 | X---.. | 3*A001168 %Y A366767 17 | 3 | 2 | -X--.. | A365655 %Y A366767 18 | 3 | 2 | * XX--.. | A075678 %Y A366767 19 |!3 | 2 | --X-.. | 3*A001168 %Y A366767 20 |!3 | 2 | X-X-.. | 3*A006770 %Y A366767 21 | 3 | 2 | -XX-.. | A365996 %Y A366767 22 | 3 | 2 | XXX-.. | A365998 %Y A366767 23 | 3 | 2 | ---X.. | A366000 %Y A366767 24 | 3 | 2 | X--X.. | A366002 %Y A366767 25 | 3 | 2 | -X-X.. | A366004 %Y A366767 26 | 3 | 2 | XX-X.. | A366006 %Y A366767 27 | 3 | 2 | * --XX.. | A365653 %Y A366767 28 | 3 | 2 | X-XX.. | A366008 %Y A366767 29 | 3 | 2 | -XXX.. | A366010 %Y A366767 30 | 3 | 2 | * XXXX.. | A365651 %Y A366767 31 | 3 | 3 | * -.-..- | A063524 %Y A366767 32 | 3 | 3 | * X.-..- | A001931 %Y A366767 33 | 3 | 3 | * -.X..- | A039742 %Y A366767 34 | 3 | 3 | * X.X..- | %Y A366767 35 | 3 | 3 | * -.-..X | A039741 %Y A366767 36 | 3 | 3 | * X.-..X | %Y A366767 37 | 3 | 3 | * -.X..X | %Y A366767 38 | 3 | 3 | * X.X..X | %Y A366767 39 |!4 | 1 | * --.... | 4*A063524 %Y A366767 40 |!4 | 1 | X-.... | 4*A000012 %Y A366767 41 | 4 | 1 | -X.... | A366341 %Y A366767 42 | 4 | 1 | * XX.... | A365562 %Y A366767 43 |!4 | 2 | * -----. | 6*A063524 %Y A366767 44 |!4 | 2 | X----. | 6*A001168 %Y A366767 45 | 4 | 2 | -X---. | A366339 %Y A366767 46 | 4 | 2 | * XX---. | A366335 %Y A366767 47 |!4 | 2 | --X--. | 6*A001168 %Y A366767 48 |!4 | 2 | X-X--. | 6*A006770 %K A366767 nonn,tabl %O A366767 1,6 %A A366767 _Pontus von Brömssen_, Oct 22 2023