cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A088616 a(n) = number of n X n (0,1) matrices A such that the 2n vectors consisting of the rows and the columns of the matrix A are all distinct.

Original entry on oeis.org

0, 0, 24, 6840, 6568800, 22080988800, 262378244741760
Offset: 1

Views

Author

Yuval Dekel and Vladeta Jovovic, Nov 17 2003

Keywords

Comments

What if you also ask that the two main diagonals are also distinct? - N. J. A. Sloane, Jan 03 2004

Crossrefs

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

Extensions

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

A089673 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 and the main antidiagonal, are all distinct.

Original entry on oeis.org

0, 0, 0, 652, 1658784, 10726929248, 172790068546048
Offset: 1

Views

Author

Vladeta Jovovic, Jan 04 2004

Keywords

Crossrefs

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

Extensions

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

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.

Original entry on oeis.org

0, 0, 0, 1692, 2329280, 13441654352, 190945826194432
Offset: 1

Views

Author

Vladeta Jovovic, Jan 04 2004

Keywords

Crossrefs

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

Extensions

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

Views

Author

Goran Kilibarda and Vladeta Jovovic, May 28 2004

Keywords

Links

Crossrefs

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

Programs

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

Formula

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).

Extensions

More terms from Robert G. Wilson v, May 29 2004
a(13) onwards from Andrew Howroyd, Jan 20 2024
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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