A390159 Array read by antidiagonals: T(n,k) is the number of k element independent vertex sets in the n X k grid graph.

1, 0, 2, 0, 2, 3, 0, 2, 8, 4, 0, 2, 22, 18, 5, 0, 2, 61, 84, 32, 6, 0, 2, 174, 405, 215, 50, 7, 0, 2, 504, 1998, 1502, 442, 72, 8, 0, 2, 1478, 10010, 10741, 4072, 792, 98, 9, 0, 2, 4374, 50726, 78052, 38438, 9091, 1292, 128, 10, 0, 2, 13035, 259289, 573797, 368868, 107004, 17791, 1969, 162, 11

Offset

1,3

Comments

Equivalently, T(n,k) is the number of ways to place k nonattacking wazirs on an n X k board.

Links

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

Eric Weisstein's World of Mathematics, Grid Graph.

Eric Weisstein's World of Mathematics, Independent Vertex Set.

Example

Array begins:
===========================================================
n\k | 1  2    3     4      5       6        7         8 ...
----+------------------------------------------------------
  1 | 1  0    0     0      0       0        0         0 ...
  2 | 2  2    2     2      2       2        2         2 ...
  3 | 3  8   22    61    174     504     1478      4374 ...
  4 | 4 18   84   405   1998   10010    50726    259289 ...
  5 | 5 32  215  1502  10741   78052   573797   4255370 ...
  6 | 6 50  442  4072  38438  368868  3581924  35093344 ...
  7 | 7 72  792  9091 107004 1280832 15516804 189681689 ...
  8 | 8 98 1292 17791 251354 3612344 52550366 771464278 ...
   ...

Crossrefs

Main diagonal is A201511.

Columns 1..8 are A000027, A001105(n-1), A172229, A172230, A172231, A172233, A172234, A178410.

Cf. A089934, A232833, A371967, A390158 (for king), A390160 (for knight).

Sequence in context: A339754 A238156 A281260 * A379638 A182406 A160706

Adjacent sequences: A390156 A390157 A390158 * A390160 A390161 A390162

Keyword

nonn,tabl

Author

Andrew Howroyd, Oct 28 2025

Status

approved