A133687 -id:A133687 - cp's OEIS frontend

A260340 Triangle read by rows: T(n,k) = number of sets of linear n-ads in k variables.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 22, 22, 1, 1, 1, 1, 130, 550, 130, 1, 1, 1, 1, 822, 16700, 16700, 822, 1, 1, 1, 1, 6202, 703297, 3330915, 703297, 6202, 1, 1, 1, 1, 52552, 38135272, 957659906, 957659906, 38135272, 52552, 1, 1

Offset: 0

N. J. A. Sloane, Jul 30 2015

T(n,k) is the number of nonequivalent n X n binary matrices with k ones in every row and column up to permutation of rows. - Andrew Howroyd, Apr 18 2020

			Triangle begins:
  1;
  1, 1;
  1, 1,    1;
  1, 1,    1,      1;
  1, 1,    6,      1,       1;
  1, 1,   22,     22,       1,      1;
  1, 1,  130,    550,     130,      1,    1;
  1, 1,  822,  16700,   16700,    822,    1, 1;
  1, 1, 6202, 703297, 3330915, 703297, 6202, 1, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..230 (rows 0..20)
P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41.

Columns k=0..4 are A000012, A000012, A002137, A333899, A333900.
Row sums are A333891.
Cf. A008300, A133687, A257463.

T(n,k) = T(n,n-k). - Andrew Howroyd, Apr 18 2020

Extended to include k=0 and more terms added by Andrew Howroyd, Apr 18 2020

A000516 Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 5, where equivalence is defined by row and column permutations. Isomorphism classes of bicolored 5-regular bipartite graphs, where isomorphism cannot exchange the colors.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 4, 51, 3529, 601055, 156473848, 54062069505, 23869437984682, 13186966476208771, 8971034249976338907, 7414924597575224629299, 7360058177440420943520750, 8683626883245180573511018830, 12066478410398147578519948851818, 19585444567548740264243478805318202

Offset: 1

Eric Rogoyski

nonn

Index entries for sequences related to Latin squares and rectangles

Column k=5 of A133687.

Cf. A000512, A000513.

Definition corrected by Brendan McKay, May 28 2006

Offset corrected and terms a(12) and beyond from Andrew Howroyd, Apr 01 2020

A000519 Number of equivalence classes of nonzero regular 0-1 matrices of order n.

Original entry on oeis.org

1, 2, 3, 5, 7, 18, 43, 313, 7525, 846992, 324127859, 403254094631, 1555631972009429, 19731915624463099552, 791773335030637885025287, 107432353216118868234728540267, 47049030539260648478475949282317451, 71364337698829887974206671525372672234854

Offset: 1

Eric Rogoyski

nonn

Previous name was: Number of different row sums among Latin squares of order n.

A regular 0-1 matrix has all row sums and column sums equal. Equivalence is defined by independently permuting rows and columns (but not by transposing). - Brendan McKay, Nov 18 2015

			For n = 4, representatives of the a(4) = 5 classes are
[1 0 0 0]  [1 1 0 0]  [1 1 0 0]  [1 1 1 0]  [1 1 1 1]
[0 1 0 0]  [1 1 0 0]  [0 1 1 0]  [1 1 0 1]  [1 1 1 1]
[0 0 1 0]  [0 0 1 1]  [0 0 1 1]  [1 0 1 1]  [1 1 1 1]
[0 0 0 1]  [0 0 1 1]  [1 0 0 1]  [0 1 1 1]  [1 1 1 1].
G.f. = x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 18*x^6 + 43*x^7 + 313*x^8 + 7525*x^9 + ...

Index entries for sequences related to Latin squares and rectangles

One less than the row sums of A133687.

Cf. A333681.

a(n) = A333681(n-1). - Andrew Howroyd, Apr 03 2020

Description changed, after discussion with Andrew Howroyd, by Brendan McKay, Nov 18 2015

Terms a(12) and beyond from Andrew Howroyd, Apr 03 2020

A333681 Number of non-isomorphic n X n binary matrices with all row and column sums equal up to permutation of rows and columns.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 19, 44, 314, 7526, 846993, 324127860, 403254094632, 1555631972009430, 19731915624463099553, 791773335030637885025288, 107432353216118868234728540268, 47049030539260648478475949282317452, 71364337698829887974206671525372672234855

Offset: 0

Andrew Howroyd, Apr 01 2020

nonn

			The a(2) = 3 matrices are:
  [0 0]  [0 1]  [1 1]
  [0 0]  [1 0]  [1 1]

Row sums of A133687.

Cf. A000519, A067209, A333160.

a(n) = A000519(n) + 1.

A333740 Number of inequivalent 2n X 2n binary matrices with rows and columns summing to n, where equivalence means permutations of rows or columns.

Original entry on oeis.org

1, 1, 2, 7, 194, 601055, 294494683312, 14584161564179926207, 80055722734531008786502722278, 53505113579082591021525466231199449015539

Offset: 0

Alois P. Heinz, Apr 03 2020

Cf. A133687.

a(n) = A133687(2n,n).

cp's OEIS Frontend

A260340 Triangle read by rows: T(n,k) = number of sets of linear n-ads in k variables.

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A000516 Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 5, where equivalence is defined by row and column permutations. Isomorphism classes of bicolored 5-regular bipartite graphs, where isomorphism cannot exchange the colors.

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A000519 Number of equivalence classes of nonzero regular 0-1 matrices of order n.

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A333681 Number of non-isomorphic n X n binary matrices with all row and column sums equal up to permutation of rows and columns.

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A333740 Number of inequivalent 2n X 2n binary matrices with rows and columns summing to n, where equivalence means permutations of rows or columns.

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