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A331654 Number of binary matrices with a total of n ones, distinct columns each with the same number of ones and distinct nonzero rows in decreasing lexicographic order. 1
1, 1, 1, 2, 1, 6, 1, 44, 6, 519, 1, 8363, 1, 163357, 9427, 3988615, 1, 117148318, 1, 3986012464, 84012192, 157783127674, 1, 7143740399835, 248686, 364166073164915, 2479642897110, 20827974319925302, 1, 1324585467847848929, 1, 92917902002561639120, 190678639438170503 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.

LINKS

Table of n, a(n) for n=1..33.

FORMULA

a(n) = Sum_{d|n} A331039(n/d, d).

EXAMPLE

The a(6) = 6 matrices are:

  [1 0 0 0 0 0]  [1 1 1]  [1 1 0]  [1 1 0]  [1 0 1]  [1 1 0]

  [0 1 0 0 0 0]  [1 0 0]  [1 0 1]  [1 0 0]  [1 0 0]  [1 0 1]

  [0 0 1 0 0 0]  [0 1 0]  [0 1 0]  [0 1 1]  [0 1 1]  [0 1 1]

  [0 0 0 1 0 0]  [0 0 1]  [0 0 1]  [0 0 1]  [0 1 0]

  [0 0 0 0 1 0]

  [0 0 0 0 0 1]

CROSSREFS

Cf. A331039.

Sequence in context: A321597 A083720 A055878 * A302690 A030304 A248779

Adjacent sequences:  A331651 A331652 A331653 * A331655 A331656 A331657

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Jan 24 2020

STATUS

approved

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Last modified August 4 13:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)