A088616 -id:A088616 - cp's OEIS frontend

A089674 a(n) = number of n X n (0,1) matrices A such that the 2n+2 vectors consisting of the rows and the columns of the matrix A, as well as the main diagonal read in the upward direction and the main antidiagonal, are all distinct.

0, 0, 0, 1692, 2329280, 13441654352, 190945826194432

Offset: 1

Vladeta Jovovic, Jan 04 2004

Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763

a(6)-a(7) from Bert Dobbelaere, May 05 2025

A094223 Number of binary n X n matrices with all rows (columns) distinct, up to permutation of columns (rows).

Original entry on oeis.org

1, 2, 7, 68, 2251, 247016, 89254228, 108168781424, 451141297789858, 6625037125817801312, 348562672319990399962384, 66545827618461283102105245248, 46543235997095840080425299916917968, 120155975713532210671953821005746669185792, 1152009540439950050422144845158703009569109376384

Offset: 0

Goran Kilibarda and Vladeta Jovovic, May 28 2004

Andrew Howroyd, Table of n, a(n) for n = 0..50
Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

Main diagonal of A059584 and A059587, A060690, A088309.

Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763

a[n_] := Sum[(-1)^(n - k)*StirlingS1[n, k]*Binomial[2^k, n], {k, 0, n}]; (* or *) a[n_] := Sum[ StirlingS1[n, k]*Binomial[2^k + n - 1, n], {k, 0, n}]; Table[ a[n], {n, 0, 12}] (* Robert G. Wilson v, May 29 2004 *)

a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k+n-1, n)); \\ Michel Marcus, Dec 17 2022

a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*binomial(2^k, n).

a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k+n-1, n).

More terms from Robert G. Wilson v, May 29 2004

a(13) onwards from Andrew Howroyd, Jan 20 2024

cp's OEIS Frontend

A089674 a(n) = number of n X n (0,1) matrices A such that the 2n+2 vectors consisting of the rows and the columns of the matrix A, as well as the main diagonal read in the upward direction and the main antidiagonal, are all distinct.

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A094223 Number of binary n X n matrices with all rows (columns) distinct, up to permutation of columns (rows).

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