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.

Showing 1-4 of 4 results.

A086922 Number of idempotent n X n (0,1) matrices over the reals.

Original entry on oeis.org

1, 2, 8, 50, 452, 5682, 96608, 2185738, 65108492
Offset: 0

Views

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 19 2003

Keywords

Comments

From Torlach Rush, Jun 18 2020: (Start)
Let m(n,k) be the number of idempotent n X n (0,1) matrices with k entries equal to 1. Then:
k | m(n,k)
-----|------------------------------------------------------
0 | 1
1 | n
2 | A028895(n - 1)
3 | 19 * A000292(n - 2)
4 | ((n - 3) (n - 2) (n - 1) (35 n - 124))/8
5 | ((n - 4) (n - 3) (n - 2) (n - 1) (631 n - 2675))/120
...
Conjecture: There is no closed form expression for this sequence.
(End)

Crossrefs

Cf. A000292, A028895, A132186, A222821.

Extensions

a(5)-a(6) from Torlach Rush, Jun 17 2020
a(7)-a(8) from A222821 added by Giovanni Resta, Jun 23 2020

A222822 Number of idempotent 3X3 0..n matrices.

Original entry on oeis.org

50, 122, 218, 344, 488, 668, 860, 1088, 1334, 1610, 1898, 2234, 2570, 2942, 3338, 3764, 4196, 4676, 5156, 5684, 6224, 6788, 7364, 8000, 8630, 9290, 9974, 10694, 11414, 12194, 12962, 13778, 14606, 15458, 16334, 17264, 18176, 19124, 20096, 21116, 22124
Offset: 1

Views

Author

R. H. Hardin Apr 09 2013

Keywords

Comments

Row 3 of A222821

Examples

			Some solutions for n=3
..0..0..0....1..0..0....1..0..0....1..0..0....1..0..0....0..0..0....0..0..0
..0..0..0....1..0..0....2..0..0....0..1..0....2..0..3....1..1..1....0..1..0
..0..0..0....0..0..0....0..0..1....2..1..0....0..0..1....0..0..0....0..1..0

Links

A222823 Number of idempotent 4X4 0..n matrices.

Original entry on oeis.org

452, 2052, 5584, 12476, 23568, 41668, 67136, 104112, 153604, 219728, 303468, 412720, 545012, 709272, 907828, 1146704, 1426212, 1759348, 2142176, 2590236, 3101848, 3686444, 4346808, 5102188, 5942936
Offset: 1

Views

Author

R. H. Hardin Apr 09 2013

Keywords

Comments

Row 4 of A222821

Examples

			Some solutions for n=3
..0..0..0..2....1..1..2..0....0..0..0..0....0..3..3..2....0..1..2..1
..0..0..3..0....0..0..0..0....2..1..3..0....0..0..0..0....0..1..1..0
..0..0..1..0....0..0..0..0....0..0..0..0....0..1..1..0....0..0..0..0
..0..0..0..1....0..0..3..1....2..0..2..1....0..0..0..1....0..0..1..1

A222824 Number of idempotent 5X5 0..n matrices.

Original entry on oeis.org

5682, 54182, 248442, 855192, 2319872, 5617912, 11946912, 23683432, 43615442, 76232022, 126661082, 203564942, 314635222, 473400002, 693921022
Offset: 1

Views

Author

R. H. Hardin Apr 09 2013

Keywords

Comments

Row 5 of A222821

Examples

			Some solutions for n=3
..1..0..0..2..0....0..0..0..0..0....0..0..0..0..0....1..0..0..0..0
..0..1..2..2..0....0..1..0..0..3....0..0..0..0..0....0..0..0..0..2
..0..0..0..0..0....2..0..0..1..3....3..1..1..0..0....0..0..0..0..3
..0..0..0..0..0....2..0..0..1..3....3..2..0..1..0....2..0..0..0..0
..0..0..2..1..1....0..0..0..0..0....2..1..0..0..1....0..0..0..0..1
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.