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A299906 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices. 4
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 16, 8, 1, 1, 16, 58, 58, 16, 1, 1, 32, 196, 344, 196, 32, 1, 1, 64, 634, 1786, 1786, 634, 64, 1, 1, 128, 1996, 8528, 13528, 8528, 1996, 128, 1, 1, 256, 6178, 38578, 90946, 90946, 38578, 6178, 256, 1, 1, 512, 18916, 168344, 564376, 833432, 564376, 168344, 18916, 512, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A (0,1) n X k matrix is lonesum if the matrix is uniquely determined by its row-sum and column-sum vectors, that is, by the sum of its rows and the sum of its columns. For example, the 2 X 3 matrix [1,1,1 / 0,1,0] is the only matrix with column-sum vector [1,2,1] and row-sum vector [3,1].

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:

  1,  1,   1,    1,     1,      1, ...,

  1,  2,   4,    8,    16,     32, ...,

  1,  4,  16,   58,   196,    634, ...,

  1,  8,  58,  344,  1786,   8528, ...,

  1, 16, 196, 1786, 13528,  90946, ...,

  1, 32, 634, 8528, 90446, 833432, ...,

  ...

MATHEMATICA

T[n_, k_] := Sum[(Binomial[j-1, k0-1] * j!^2 * StirlingS2[k+1, j+1] * StirlingS2[n+1, j+1])/k0!, {k0, 0, k}, {j, k0, Min[k, n]}]; Table[T[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 24 2018 *)

CROSSREFS

Cf. A299904, A299905.

See A299907 for main diagonal (i.e. square matrices).

See also A000629, A221961 for symmetric square matrices.

See A099594 for lonesum (0,1) matrices.

Sequence in context: A099594 A255256 A328887 * A117401 A144324 A331406

Adjacent sequences:  A299903 A299904 A299905 * A299907 A299908 A299909

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 23 2018

EXTENSIONS

More terms from Jean-François Alcover, Feb 24 2018

Name corrected by Alexander Karpov, Oct 19 2019

STATUS

approved

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Last modified May 8 05:46 EDT 2021. Contains 343653 sequences. (Running on oeis4.)