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A299904 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 1. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A129533 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

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Last modified May 13 14:29 EDT 2021. Contains 343859 sequences. (Running on oeis4.)