A390158 Array read by antidiagonals: T(n,k) is the number of ways to place k nonattacking kings on a n X k board.

1, 0, 2, 0, 0, 3, 0, 0, 4, 4, 0, 0, 8, 12, 5, 0, 0, 9, 34, 24, 6, 0, 0, 15, 79, 105, 40, 7, 0, 0, 16, 194, 454, 248, 60, 8, 0, 0, 24, 408, 1974, 1566, 490, 84, 9, 0, 0, 25, 926, 8544, 9856, 4103, 858, 112, 10, 0, 0, 35, 1847, 37282, 62266, 34475, 9009, 1379, 144, 11

Offset

1,3

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  0   0    0     0       0        0         0 ...
  2 | 2  0   0    0     0       0        0         0 ...
  3 | 3  4   8    9    15      16       24        25 ...
  4 | 4 12  34   79   194     408      926      1847 ...
  5 | 5 24 105  454  1974    8544    37282    162531 ...
  6 | 6 40 248 1566  9856   62266   394202   2501726 ...
  7 | 7 60 490 4103 34475  291908  2484382  21243084 ...
  8 | 8 84 858 9009 95466 1021254 10999618 119138166 ...
   ...

Crossrefs

Main diagonal is A201513.

Row 3 is A135276(k+1).

Columns 1..8 are A000027, A046092(n-2), A172202, A172203, A172204, A172205, A172206, A172261.

Cf. A245013, A193580, A350819.

Sequence in context: A175676 A384627 A392675 * A035377 A136274 A290976

Adjacent sequences: A390155 A390156 A390157 * A390159 A390160 A390161

Keyword

nonn,tabl

Author

Andrew Howroyd, Oct 27 2025

Status

approved