A120733 -id:A120733 - cp's OEIS frontend

A321717 Number of non-normal (0,1) semi-magic rectangles with sum of all entries equal to n.

1, 1, 4, 8, 39, 122, 950, 5042, 45594, 366243, 3858148, 39916802, 494852628, 6227020802, 88543569808, 1308012219556, 21086562956045, 355687428096002, 6427672041650478, 121645100408832002, 2437655776358606198, 51091307191310604724, 1125098543553717372868, 25852016738884976640002, 620752122372339473623314, 15511210044577707470250243

Offset: 0

Gus Wiseman, Nov 18 2018

nonn

A non-normal semi-magic rectangle is a nonnegative integer matrix with row sums and column sums all equal to d, for some d|n.

Rectangles must be of size k X m where k and m are divisors of n and k*m >= n. This implies that a(p) = p! + 2 for p prime since the only allowable rectangles are of sizes 1 X 1, 1 X p, p X 1 and p X p. There are no 1 X 1 rectangle that satisfies the condition. The 1 X p and p X 1 rectangles are [1....1] and its transpose, the p X p rectangle are necessarily permutation matrices and there are p! permutation matrices of size p X p. It also shows that a(n) >= n! + 2 for n > 1. - Chai Wah Wu, Jan 13 2019

			The a(3) = 8 semi-magic rectangles:
  [1 1 1]
.
  [1] [1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
  [1] [0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
  [1] [0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]

Max Alekseyev, Table of n, a(n) for n = 0..71
Wikipedia, Magic square

Cf. A006052, A007016, A068313, A101370, A120733, A271103, A319056.

Cf. A321718, A321719, A321720, A321721, A321722, A321723, A321724, A321725.

prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],SameQ@@Total/@prs2mat[#],SameQ@@Total/@Transpose[prs2mat[#]]]&]],{n,5}]

a(p) = p! + 2 for p prime. a(n) >= n! + 2 for n > 1. - Chai Wah Wu, Jan 13 2019

a(7) from Chai Wah Wu, Jan 13 2019
a(8)-a(13) from Chai Wah Wu, Jan 14 2019
a(14)-a(15) from Chai Wah Wu, Jan 15 2019
a(16)-a(19) from Chai Wah Wu, Jan 16 2019
Terms a(20) onward from Max Alekseyev, Dec 04 2024

A068313 Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums.

Original entry on oeis.org

1, 4, 15, 82, 457, 3231, 24055, 209375, 1955288, 20455936, 229830841, 2828166755, 37228913365, 528635368980, 7990596990430, 128909374528433, 2202090635802581, 39837079499488151, 759320365206705013, 15234890522990662422, 320634889654149218205, 7068984425261215971205

Offset: 1

Axel Kohnert (axel.kohnert(AT)uni-bayreuth.de), Feb 25 2002

nonn

This is the sum over the matrix of base change from the elementary symmetric functions to the monomial symmetric functions.

			a(2) = 4 because there are 4 different 0-1 matrices of weight 2: 1 10 01 11,1, 01, 10.
From _Gus Wiseman_, Nov 15 2018: (Start)
The a(3) = 15 matrices:
  [1 1 1]
.
  [1 1] [1 1 0] [1 0 1] [0 1 1]
  [1 0] [0 0 1] [0 1 0] [1 0 0]
.
  [1] [1 0] [1 0] [1 0 0] [1 0 0] [0 1] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
  [1] [1 0] [0 1] [0 1 0] [0 0 1] [1 0] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
  [1] [0 1] [1 0] [0 0 1] [0 1 0] [1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
(End)

I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford 1979, p. 57.

Ludovic Schwob, Table of n, a(n) for n = 1..37
Ludovic Schwob, On the enumeration of double cosets and self-inverse double cosets, arXiv:2506.04007 [math.CO], 2025. See p. 14.

Cf. A000219, A001970, A007716, A049311, A101370, A117433, A120733, A321646, A321652, A321653, A321654.

prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],OrderedQ[Total/@prs2mat[#]],OrderedQ[Total/@T[prs2mat[#]]]]&]],{n,5}] (* Gus Wiseman, Nov 15 2018 *)

Name changed by Gus Wiseman, Nov 15 2018

a(20) onwards from Ludovic Schwob, Oct 13 2023

A321718 Number of coupled non-normal semi-magic rectangles with sum of entries equal to n.

Original entry on oeis.org

1, 1, 5, 9, 44, 123, 986, 5043, 45832, 366300, 3862429, 39916803, 495023832, 6227020803, 88549595295, 1308012377572, 21086922542349, 355687428096003, 6427700493998229, 121645100408832003, 2437658338007783347, 51091307195905020227, 1125098837523651728389, 25852016738884976640003, 620752163206546966698620, 15511210044577707492319496

Offset: 0

Gus Wiseman, Nov 18 2018

nonn

A coupled non-normal semi-magic rectangle is a nonnegative integer matrix with equal row sums and equal column sums. The common row sum may be different from the common column sum.

Rectangles must be of size k X m where k and m are divisors of n. This implies that a(p) = p! + 3 for p prime since the only allowable rectangles are of sizes 1 X 1, 1 X p, p X 1 and p X p. The 1 X 1 square is [p], the 1 X p and p X 1 rectangles are [1,...,1] and its transpose and the p X p squares are necessarily permutation matrices and there are p! permutation matrices of size p X p. Also, a(n) >= n! + 3 for n > 1. - Chai Wah Wu, Jan 15 2019

			The a(3) = 9 coupled semi-magic rectangles:
  [3] [1 1 1]
.
  [1] [1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
  [1] [0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
  [1] [0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]

Max Alekseyev, Table of n, a(n) for n = 0..69
Wikipedia, Magic square

Cf. A006052, A120733, A271103, A319056, A321654.

Cf. A321717, A321719, A321720, A321721, A321722, A321724, A321724.

prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
Table[Length[Select[multsubs[Tuples[Range[n],2],n],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],SameQ@@Total/@prs2mat[#],SameQ@@Total/@Transpose[prs2mat[#]]]&]],{n,5}]

a(p) = p! + 3 for p prime. a(n) >= n! + 3 for n > 1. - Chai Wah Wu, Jan 15 2019

a(7)-a(15) from Chai Wah Wu, Jan 15 2019
a(16)-a(19) from Chai Wah Wu, Jan 16 2019
Terms a(20) onward from Max Alekseyev, Dec 04 2024

A323351 Number of ways to fill a (not necessarily square) matrix with n zeros and ones.

Original entry on oeis.org

1, 2, 8, 16, 48, 64, 256, 256, 1024, 1536, 4096, 4096, 24576, 16384, 65536, 131072, 327680, 262144, 1572864, 1048576, 6291456, 8388608, 16777216, 16777216, 134217728, 100663296, 268435456, 536870912, 1610612736, 1073741824, 8589934592, 4294967296, 25769803776

Offset: 0

Gus Wiseman, Jan 15 2019

nonn

			The a(3) = 16 matrices:
  [000] [001] [010] [011] [100] [101] [110] [111]
.
  [0] [0] [0] [0] [1] [1] [1] [1]
  [0] [0] [1] [1] [0] [0] [1] [1]
  [0] [1] [0] [1] [0] [1] [0] [1]

Cf. A000005, A049311, A120733, A323295, A323300.

Mathematica
```
Table[2^n*DivisorSigma[0,n],{n,10}]
```

a(n) = if (n==0, 1, 2^n*numdiv(n)); \\ Michel Marcus, Jan 15 2019

a(n) = 2^n * A000005(n) for n > 0, a(0) = 1.

G.f.: 1 + Sum_{k>=1} 2^k*x^k/(1 - 2^k*x^k). - Ilya Gutkovskiy, May 23 2019

A057150 Triangle read by rows: T(n,k) = number of k X k binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 5, 2, 1, 0, 0, 4, 11, 2, 1, 0, 0, 3, 21, 14, 2, 1, 0, 0, 1, 34, 49, 15, 2, 1, 0, 0, 1, 33, 131, 69, 15, 2, 1, 0, 0, 0, 33, 248, 288, 79, 15, 2, 1, 0, 0, 0, 19, 410, 840, 420, 82, 15, 2, 1, 0, 0, 0, 14, 531, 2144, 1744, 497, 83, 15, 2, 1

Offset: 1

Vladeta Jovovic, Aug 14 2000

Also the number of non-isomorphic set multipartitions (multisets of sets) of weight n with k parts and k vertices. - Gus Wiseman, Nov 14 2018

			[1], [0,1], [0,1,1], [0,1,2,1], [0,0,5,2,1], [0,0,4,11,2,1], ...;
There are 8 square binary matrices with 5 ones, with no zero rows or columns, up to row and column permutation: 5 of size 3 X 3:
[0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 1 0] [0 1 1] [0 1 1] [1 1 0]
[1 1 1] [1 1 1] [1 0 1] [1 1 0] [1 1 0]
2 of size 4 X 4:
[0 0 0 1] [0 0 0 1]
[0 0 0 1] [0 0 1 0]
[0 0 1 0] [0 1 0 0]
[1 1 0 0] [1 0 0 1]
and 1 of size 5 X 5:
[0 0 0 0 1]
[0 0 0 1 0]
[0 0 1 0 0]
[0 1 0 0 0]
[1 0 0 0 0].
From _Gus Wiseman_, Nov 14 2018: (Start)
Triangle begins:
   1
   0   1
   0   1   1
   0   1   2   1
   0   0   5   2   1
   0   0   4  11   2   1
   0   0   3  21  14   2   1
   0   0   1  34  49  15   2   1
   0   0   1  33 131  69  15   2   1
   0   0   0  33 248 288  79  15   2   1
Non-isomorphic representatives of the multiset partitions counted in row 6 {0,0,4,11,2,1} are:
  {{12}{13}{23}}  {{1}{1}{1}{234}}  {{1}{2}{3}{3}{45}}  {{1}{2}{3}{4}{5}{6}}
  {{1}{23}{123}}  {{1}{1}{24}{34}}  {{1}{2}{3}{5}{45}}
  {{13}{23}{23}}  {{1}{1}{4}{234}}
  {{3}{23}{123}}  {{1}{2}{34}{34}}
                  {{1}{3}{24}{34}}
                  {{1}{3}{4}{234}}
                  {{1}{4}{24}{34}}
                  {{1}{4}{4}{234}}
                  {{2}{4}{12}{34}}
                  {{3}{4}{12}{34}}
                  {{4}{4}{12}{34}}
(End)

Row sums give A057151.
Cf. A049311, A056037, A056079, A056080, A057149, A057151, A057152.
Cf. A007716, A048291, A054976, A101370, A104601, A104602, A120732, A120733, A135588, A319616, A321609, A321615.

permcount[v_List] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
c[p_List, q_List, k_] := SeriesCoefficient[Product[Product[(1 + O[x]^(k + 1) + x^LCM[p[[i]], q[[j]]])^GCD[p[[i]], q[[j]]], {j, 1, Length[q]}], {i, 1, Length[p]}], {x, 0, k}];
M[m_, n_, k_] := M[m, n, k] = Module[{s = 0}, Do[Do[s += permcount[p]* permcount[q]*c[p, q, k], {q, IntegerPartitions[n]}], {p, IntegerPartitions[m]}]; s/(m!*n!)];
T[n_, k_] := M[k, k, n] - 2*M[k, k - 1, n] + M[k - 1, k - 1, n];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 10 2019, after Andrew Howroyd *)

\\ See A321609 for M.
T(n,k) = M(k,k,n) - 2*M(k,k-1,n) + M(k-1,k-1,n); \\ Andrew Howroyd, Nov 14 2018

Duplicate seventh row removed by Gus Wiseman, Nov 14 2018

A323295 Number of ways to fill a matrix with the first n positive integers.

Original entry on oeis.org

1, 1, 4, 12, 72, 240, 2880, 10080, 161280, 1088640, 14515200, 79833600, 2874009600, 12454041600, 348713164800, 5230697472000, 104613949440000, 711374856192000, 38414242234368000, 243290200817664000, 14597412049059840000, 204363768686837760000

Offset: 0

Gus Wiseman, Jan 12 2019

nonn

			The a(4) = 72 matrices consist of:
  24 row/column permutations of [1 2 3 4]
+
  4 row/column permutations of [1 2]
                               [3 4]
+
  4 row/column permutations of [1 2]
                               [4 3]
+
  4 row/column permutations of [1 3]
                               [2 4]
+
  4 row/column permutations of [1 3]
                               [4 2]
+
  4 row/column permutations of [1 4]
                               [2 3]
+
  4 row/column permutations of [1 4]
                               [3 2]
+
  24 row/column permutations of [1]
                                [2]
                                [3]
                                [4]

Cf. A000005, A000142, A038041, A053529, A057625, A061095, A120733, A121860.

Cf. A323300, A323301, A323307, A323351.

Join[{1}, Table[DivisorSigma[0, n]*n!, {n, 30}]]

a(n) = if (n==0, 1, numdiv(n)*n!); \\ Michel Marcus, Jan 15 2019

a(n) = A000005(n) * n! for n > 0, a(0) = 1.

E.g.f.: 1 + Sum_{k>=1} x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 13 2019

A104601 Triangle T(r,n) read by rows: number of n X n (0,1)-matrices with exactly r entries equal to 1 and no zero row or columns.

Original entry on oeis.org

1, 0, 2, 0, 4, 6, 0, 1, 45, 24, 0, 0, 90, 432, 120, 0, 0, 78, 2248, 4200, 720, 0, 0, 36, 5776, 43000, 43200, 5040, 0, 0, 9, 9066, 222925, 755100, 476280, 40320, 0, 0, 1, 9696, 727375, 6700500, 13003620, 5644800, 362880, 0, 0, 0, 7480, 1674840

Offset: 1

Ralf Stephan, Mar 27 2005

			1
0,2
0,4,6
0,1,45,24
0,0,90,432,120
0,0,78,2248,4200,720
0,0,36,5776,43000,43200,5040
0,0,9,9066,222925,755100,476280,40320
0,0,1,9696,727375,6700500,13003620,5644800,362880
0,0,0,7480,1674840,37638036,179494350,226262400,71850240,3628800

M. Maia and M. Mendez, On the arithmetic product of combinatorial species, arXiv:math/0503436 [math.CO], 2005.

Right-edge diagonals include A000142, A055602, A055603. Row sums are in A104602.
Column sums are in A048291. The triangle read by columns = A055599.
Cf. A049311, A054976, A057150, A057151, A101370, A120732, A120733, A138178, A316983, A319616.

t[r_, n_] := Sum[ Sum[ (-1)^(2n - d - k/d)*Binomial[n, d]*Binomial[n, k/d]*Binomial[k, r], {d, Divisors[k]}], {k, r, n^2}]; Flatten[ Table[t[r, n], {r, 1, 10}, {n, 1, r}]] (* Jean-François Alcover, Jun 27 2012, from formula *)
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],Union[First/@#]==Union[Last/@#]==Range[k]&]],{n,6},{k,n}] (* Gus Wiseman, Nov 14 2018 *)

T(r, n) = Sum{l>=r, Sum{d|l, (-1)^(2n-d-l/d)*C(n, d)*C(n, l/d)*C(l, r) }}.

E.g.f.: Sum(((1+x)^n-1)^n*exp((1-(1+x)^n)*y)*y^n/n!,n=0..infinity). - Vladeta Jovovic, Feb 24 2008

A135588 Number of symmetric (0,1)-matrices with exactly n entries equal to 1 and no zero rows or columns.

Original entry on oeis.org

1, 1, 2, 6, 20, 74, 302, 1314, 6122, 29982, 154718, 831986, 4667070, 27118610, 163264862, 1013640242, 6488705638, 42687497378, 288492113950, 1998190669298, 14177192483742, 102856494496050, 762657487965086, 5771613810502002, 44555989658479726, 350503696871063138

Offset: 0

Vladeta Jovovic, Feb 25 2008, Mar 03 2008, Mar 04 2008

nonn

			From _Gus Wiseman_, Nov 14 2018: (Start)
The a(4) = 20 matrices:
  [11]
  [11]
.
  [110][101][100][100][011][010][010][001][001]
  [100][010][011][001][100][110][101][010][001]
  [001][100][010][011][100][001][010][101][110]
.
  [1000][1000][1000][1000][0100][0100][0010][0010][0001][0001]
  [0100][0100][0010][0001][1000][1000][0100][0001][0100][0010]
  [0010][0001][0100][0010][0010][0001][1000][1000][0010][0100]
  [0001][0010][0001][0100][0001][0010][0001][0100][1000][1000]
(End)

Alois P. Heinz, Table of n, a(n) for n = 0..721 (first 51 terms from Vincenzo Librandi)

Row sums of A135589.

Cf. A049311, A054976, A101370, A104601, A104602, A120733, A138178, A283877, A316983, A320796, A321401, A321405.

Table[Sum[SeriesCoefficient[(1+x)^k*(1+x^2)^(k*(k-1)/2)/2^(k+1),{x,0,n}],{k,0,Infinity}],{n,0,20}] (* Vaclav Kotesovec, Jul 02 2014 *)
Join[{1},  Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], Sort[Reverse/@#]==#]&]], {n, 5}]] (* Gus Wiseman, Nov 14 2018 *)

G.f.: Sum_{n>=0} (1+x)^n*(1+x^2)^binomial(n,2)/2^(n+1).

G.f.: Sum_{n>=0} (Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*(1+x)^k*(1+x^2)^binomial(k,2)).

A321645 Number of distinct row/column permutations of plane partitions of n.

Original entry on oeis.org

1, 1, 3, 11, 32, 96, 290, 864, 2502, 7134, 20081

Offset: 0

Gus Wiseman, Nov 15 2018

			The a(3) = 11 permutations of plane partitions:
  [3] [2 1] [1 2] [1 1 1]
.
  [2] [1 1] [1 1] [1] [1 0] [0 1]
  [1] [1 0] [0 1] [2] [1 1] [1 1]
.
  [1]
  [1]
  [1]

Cf. A000219, A001970, A007716, A008480, A068313, A114736, A120733, A316983, A319646.

Cf. A321646, A321647, A321648, A321652, A321653, A321655.

submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{_,x_,W___}}/;submultisetQ[{Z},{W}]]];
multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
Table[Length[Select[multsubs[Tuples[Range[n],2],n],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],OrderedQ[Sort[Map[Last,GatherBy[Sort[Reverse/@#],First],{2}],submultisetQ],submultisetQ],OrderedQ[Sort[Sort/@Map[Last,GatherBy[#,First],{2}],submultisetQ],submultisetQ]]&]],{n,6}]

A323307 Number of ways to fill a matrix with the parts of a multiset whose multiplicities are the prime indices of n.

Original entry on oeis.org

1, 1, 2, 4, 2, 6, 3, 12, 18, 12, 2, 36, 4, 10, 20, 72, 2, 60, 4, 40, 60, 24, 3, 120, 80, 14, 360, 120, 4, 240, 2, 240, 42, 32, 70, 720, 6, 27, 112, 480, 2, 210, 4, 84, 420, 40, 4, 1440, 280, 280, 108, 224, 5, 1260, 224, 420, 180, 22, 2, 840, 6, 72, 1680, 2880

Offset: 1

Gus Wiseman, Jan 13 2019

nonn

This multiset (row n of A305936) is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.

			The a(22) = 24 matrices:
  [111112] [111121] [111211] [112111] [121111] [211111]
.
  [111] [111] [111] [112] [121] [211]
  [112] [121] [211] [111] [111] [111]
.
  [11] [11] [11] [11] [12] [21]
  [11] [11] [12] [21] [11] [11]
  [12] [21] [11] [11] [11] [11]
.
  [1] [1] [1] [1] [1] [2]
  [1] [1] [1] [1] [2] [1]
  [1] [1] [1] [2] [1] [1]
  [1] [1] [2] [1] [1] [1]
  [1] [2] [1] [1] [1] [1]
  [2] [1] [1] [1] [1] [1]

Gus Wiseman, The a(27) = 360 matrix-arrangements of (1,1,2,2,3,3).

Cf. A007716, A056239, A112798, A120733, A181821, A305936, A318283, A318284, A323295, A323300, A323351.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS,facs[n],{2}]),SameQ@@Length/@#&];
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
Array[Length[ptnmats[Times@@Prime/@nrmptn[#]]]&,30]

a(n) = A318762(n) * A000005(A056239(n)).

cp's OEIS Frontend

A321717 Number of non-normal (0,1) semi-magic rectangles with sum of all entries equal to n.

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A068313 Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums.

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A321718 Number of coupled non-normal semi-magic rectangles with sum of entries equal to n.

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A323351 Number of ways to fill a (not necessarily square) matrix with n zeros and ones.

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A057150 Triangle read by rows: T(n,k) = number of k X k binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

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A323295 Number of ways to fill a matrix with the first n positive integers.

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A104601 Triangle T(r,n) read by rows: number of n X n (0,1)-matrices with exactly r entries equal to 1 and no zero row or columns.

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A135588 Number of symmetric (0,1)-matrices with exactly n entries equal to 1 and no zero rows or columns.

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