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A241956 Number of inequivalent m X n binary matrices, where equivalence means permutations of rows or columns. Presented in diagonal order, with (m,n)=(1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ... . 2
2, 3, 3, 4, 7, 4, 5, 13, 13, 5, 6, 22, 36, 22, 6, 7, 34, 87, 87, 34, 7, 8, 50, 190, 317, 190, 50, 8, 9, 70, 386, 1053, 1053, 386, 70, 9, 10, 95, 734, 3250, 5624, 3250, 734, 95, 10, 11, 125, 1324, 9343, 28576, 28576, 9343, 1324, 125, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Same as A028657 without first row and column.

LINKS

Alois P. Heinz, Antidiagonals m = 1..45, flattened

Adalbert Kerber, Applied Finite Group Actions, second edition, Springer-Verlag, (1999). See table under Corollary 2.3.1 on page 68.

Various authors, How many n-by-m binary matrices are there up to row and column permutations

EXAMPLE

The array begins:

2 3 4 5 6 7 8 9 ...

3 7 13 22 34 50 70 95 ...

4 13 36 87 190 386 734 1324 ...

5 22 87 317 1053 3250 9343 25207 ...

6 34 190 1053 5624 28576 136758 613894 ...

7 50 386 3250 28576 251610 2141733 17256831 ...

8 70 734 9343 136758 2141733 33642 660508 147108 ...

9 95 1324 25207 613894 17256831 508147108 14685630688 ...

(cf. A028657).

MAPLE

b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i<1, [], [seq(map(

      p->`if`(j=0, p, [p[], [i, j]]), b(n-i*j, i-1))[], j=0..n/i)]))

    end:

g:= proc(n, k) option remember; add(add(2^add(add(i[2]*j[2]*

      igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)

      /mul(i[1]^i[2]*i[2]!, i=t), t=b(n+k$2)), s=b(n$2))

    end:

A:= (m, n)-> g(min(m, n), abs(m-n)):

seq(seq(A(m, 1+d-m), m=1..d), d=1..12); # Alois P. Heinz, Aug 13 2014

CROSSREFS

Cf. A002724.

Sequence in context: A185738 A239361 A266362 * A227125 A248944 A267245

Adjacent sequences:  A241953 A241954 A241955 * A241957 A241958 A241959

KEYWORD

nonn,tabl

AUTHOR

Don Knuth, Aug 09 2014

STATUS

approved

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Last modified July 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)