A299904 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 1.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 7, 13, 7, 0, 0, 15, 45, 45, 15, 0, 0, 31, 145, 229, 145, 31, 0, 0, 63, 453, 1065, 1065, 453, 63, 0, 0, 127, 1393, 4717, 6901, 4717, 1393, 127, 0, 0, 255, 4245, 20265, 41505, 41505, 20265, 4245, 255, 0, 0, 511, 12865, 85309, 237685, 329461, 237685, 85309, 12865, 511, 0

Offset

0,8

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,...,
0,1,3,7,15,31,...,
0,3,13,45,145,453,...,
0,7,45,229,1065,4717,...,
0,15,145,1065,6901,41505,...,
0,31,453,4717,41505,32946,...,
...

Mathematica

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

Crossrefs

Cf. A299905, A299906.

Sequence in context: A360849 A155999 A338034 * A221768 A283071 A060523

Adjacent sequences: A299901 A299902 A299903 * A299905 A299906 A299907

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 23 2018

Extensions

More terms from Jean-François Alcover, Feb 24 2018

Status

approved