A299905 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 2.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 50, 108, 50, 0, 0, 0, 0, 180, 660, 660, 180, 0, 0, 0, 0, 602, 3420, 5714, 3420, 602, 0, 0, 0, 0, 1932, 16212, 40860, 40860, 16212, 1932, 0, 0, 0, 0, 6050, 72828, 262010, 391500, 262010, 72828, 6050, 0, 0

Offset

0,13

Links

Table of n, a(n) for n=0..65.

Ken Kamano, Lonesum decomposable matrices, arXiv:1701.07157 [math.CO], 2017. Also Discrete Math., 341 (2018), 341-349.

Example

Array begins:
0,0,0,0,0,0,...,
0,0,0,0,0,0,...,
0,0,2,12,50,180,...,
0,0,12,108,660,3420,...,
0,0,50,660,5714,40860,...,
0,0,180,3420,40860,39150,...,
...

Mathematica

T[n_, k_] := Sum[(1/2)*(j - 1 )*j!^2*StirlingS2[k + 1, j + 1]*StirlingS2[n + 1, j + 1], {j, 2, Min[k, n]}]; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 24 2018 *)

Crossrefs

Cf. A299904, A299906.

Sequence in context: A184366 A230614 A230730 * A225783 A135468 A003196

Adjacent sequences: A299902 A299903 A299904 * A299906 A299907 A299908

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 23 2018

Extensions

More terms from Jean-François Alcover, Feb 24 2018

Status

approved