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.

Previous Showing 11-15 of 15 results.

A331510 Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 3, 1, 0, 1, 1, 5, 4, 0, 0, 1, 1, 7, 12, 3, 0, 0, 1, 1, 11, 36, 23, 1, 0, 0, 1, 1, 15, 124, 191, 30, 0, 0, 0, 1, 1, 22, 412, 2203, 837, 23, 0, 0, 0, 1, 1, 30, 1500, 31313, 41664, 2688, 12, 0, 0, 0, 1
Offset: 0

Views

Author

Andrew Howroyd, Jan 18 2020

Keywords

Examples

			Array begins:
=================================
n\k | 0 1 2 3  4   5    6   7
----+----------------------------
  0 | 1 1 1 1  1   1    1   1 ...
  1 | 1 1 2 3  5   7   11  15 ...
  2 | 1 0 1 4 12  36  124 412 ...
  3 | 1 0 0 3 23 191 2203 ...
  4 | 1 0 0 1 30 837 ...
  5 | 1 0 0 0 23 ...
  ...
The A(2,3) = 4 matrices are:
  [1 1 1]  [1 1 0]  [1 1 1]  [1 1 0]
  [1 0 0]  [1 0 1]  [1 1 0]  [1 0 1]
  [0 1 0]  [0 1 0]  [0 0 1]  [0 1 1]
  [0 0 1]  [0 0 1]

Crossrefs

Rows n=1..3 are A000041, A331717, A331718.
Column k=5 is A331719.
Cf. A188445, A330942, A331461, A331508, A331509.

Formula

A(n,k) = 0 for k > 0, n > 2^(k-1).
A(n,k) = A(2^(k-1) - n, k) for k > 0, n <= 2^(k-1).

Extensions

a(58)-a(65) from Andrew Howroyd, Feb 08 2020

A331127 Number of n-regular hypergraphs on 5 labeled vertices.

Original entry on oeis.org

1, 52, 1088, 11301, 67198, 250735, 621348, 1058139, 1261184, 1058139, 621348, 250735, 67198, 11301, 1088, 52, 1
Offset: 0

Views

Author

Andrew Howroyd, Jan 10 2020

Keywords

Comments

The sums of all terms is 5280908 = A319190(5) + 1. The extra 1 comes from the empty hypergraph.

Crossrefs

Column k=5 of A188445.
Cf. A319190, A331129.

A188446 Number of (4*n) X n binary arrays with nonzero rows in decreasing order and 4 ones in every column.

Original entry on oeis.org

1, 0, 0, 1, 278, 67198, 24537905, 13744869502, 11385203921707, 13429702800066408, 21828741452174445770, 47540906064229854124913, 135469436416591290078176485, 494882516747849393466094870718, 2277287830010010200588821272208162, 13000224127787800362702159372817442122
Offset: 0

Views

Author

R. H. Hardin, Mar 31 2011

Keywords

Examples

			Some solutions for 16 X 4:
  1 1 1 0     1 1 1 1     1 1 1 1     1 1 1 1     1 1 1 0
  1 1 0 1     1 0 1 0     1 1 1 0     1 1 1 0     1 1 0 0
  1 0 1 0     1 0 0 1     1 0 1 1     1 0 1 0     1 0 1 1
  1 0 0 1     1 0 0 0     1 0 0 0     1 0 0 1     1 0 0 1
  0 1 1 0     0 1 1 1     0 1 0 1     0 1 0 1     0 1 1 0
  0 1 0 1     0 1 1 0     0 1 0 0     0 1 0 0     0 1 0 1
  0 0 1 1     0 1 0 0     0 0 1 1     0 0 1 0     0 0 1 0
  0 0 0 0     0 0 0 1     0 0 0 0     0 0 0 1     0 0 0 1
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0

Links

Crossrefs

Row 4 of A188445.

Extensions

a(0)=1 prepended and terms a(9) and beyond from Andrew Howroyd, Dec 15 2018

A331129 Number of n-regular hypergraphs on 6 labeled vertices.

Original entry on oeis.org

1, 203, 19232, 904580, 24537905, 425677958, 5064948309, 43418499491, 277921468720, 1364366313210, 5242437628968, 16014094403124, 39357448344781, 78528595223300, 128048008057615, 171403741608326, 188847475249322, 171403741608326, 128048008057615, 78528595223300
Offset: 0

Views

Author

Andrew Howroyd, Jan 10 2020

Keywords

Comments

The sums of all terms is A319190(6) + 1. The extra 1 comes from the empty hypergraph.

Links

Crossrefs

Column k=6 of A188445.
Cf. A319190, A331127.

Extensions

Terms a(16) and beyond from Andrew Howroyd, Mar 12 2020

A188447 Number of (5*n) X n binary arrays with nonzero rows in decreasing order and 5 ones in every column.

Original entry on oeis.org

1, 0, 0, 0, 205, 250735, 425677958, 1184910460297, 5319037255069867, 37061043058189077109, 385952934535384722609921, 5808709067366205646755198576, 122705633165265276505954301866183, 3547341635706102198376777462145800378, 137294155514669462885867305539515979061866
Offset: 0

Views

Author

R. H. Hardin, Mar 31 2011

Keywords

Examples

			Some solutions for 20 X 4:
  1 1 1 1     1 1 1 0     1 1 1 1     1 1 1 0     1 1 0 1
  1 1 1 0     1 1 0 1     1 1 0 1     1 1 0 1     1 0 1 1
  1 1 0 1     1 0 1 1     1 1 0 0     1 0 1 1     1 0 1 0
  1 0 1 1     1 0 1 0     1 0 1 0     1 0 1 0     1 0 0 1
  1 0 0 0     1 0 0 1     1 0 0 1     1 0 0 0     1 0 0 0
  0 1 1 0     0 1 1 0     0 1 1 0     0 1 1 1     0 1 1 1
  0 1 0 1     0 1 0 1     0 1 0 1     0 1 1 0     0 1 1 0
  0 0 1 1     0 1 0 0     0 0 1 1     0 1 0 1     0 1 0 1
  0 0 0 0     0 0 1 1     0 0 1 0     0 0 0 1     0 1 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 1 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0

Links

Crossrefs

Row 5 of A188445.

Extensions

a(0)=1 prepended and terms a(9) and beyond from Andrew Howroyd, Dec 15 2018
Previous Showing 11-15 of 15 results.

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