A391823 Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from top row to lower right corner, and no 1 having more than two 1's adjacent.

1, 2, 1, 3, 5, 1, 4, 11, 7, 1, 5, 21, 28, 11, 1, 6, 38, 80, 63, 18, 1, 7, 66, 200, 259, 138, 29, 1, 8, 112, 469, 896, 775, 298, 47, 1, 9, 187, 1064, 2821, 3643, 2223, 642, 76, 1, 10, 309, 2359, 8515, 15350, 13930, 6336, 1371, 123, 1, 11, 507, 5144, 24940, 62079, 76848, 53065, 17796, 2908, 199, 1

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals)

Example

Array begins:
===========================================================
n\k | 1  2    3     4      5       6        7         8 ...
----+------------------------------------------------------
  1 | 1  2    3     4      5       6        7         8 ...
  2 | 1  5   11    21     38      66      112       187 ...
  3 | 1  7   28    80    200     469     1064      2359 ...
  4 | 1 11   63   259    896    2821     8515     24940 ...
  5 | 1 18  138   775   3643   15350    62079    245117 ...
  6 | 1 29  298  2223  13930   76848   405512   2108910 ...
  7 | 1 47  642  6336  53065  381729  2583720  17293440 ...
  8 | 1 76 1371 17796 200834 1904232 16613952 142650787 ...
  ...

Crossrefs

Main diagonal is A163694.

Columns 1..10 are A000012, A163695, A163696, A163697, A163698, A163699, A163700, A163701, A163702, A163703.

Rows 1..10 are A000027, A163704, A163705, A163706, A163707, A163708, A163709, A163710, A163711, A163712.

Cf. A391489, A391818, A391819, A391820, A391822.

Sequence in context: A118243 A210233 A347667 * A297582 A134081 A134247

Adjacent sequences: A391820 A391821 A391822 * A391824 A391825 A391826

Keyword

nonn,tabl

Author

Andrew Howroyd, Dec 22 2025

Status

approved