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 1-3 of 3 results.

A284990 Triangle T(n,t) read by rows: the number of n X n {0,1} matrices with trace t where each row sum and each column sum is 3.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 6, 8, 9, 44, 210, 420, 610, 540, 216, 7570, 33120, 66870, 82080, 66870, 33120, 7570, 1975560, 8171730, 15729000, 18433415, 14372820, 7499940, 2398900, 357435, 749649145, 2971510080, 5508175260, 6267658544, 4815171270, 2570369760, 932429820, 209185200, 22040361
Offset: 0

Views

Author

R. J. Mathar, Apr 07 2017

Keywords

Examples

			0:        1
1:        0       0
2:        0       0        0
3:        0       0        0        1
4:        1       0        6        8        9
5:       44     210      420      610      540     216
6:     7570   33120    66870    82080    66870   33120    7570
7:  1975560 8171730 15729000 18433415 14372820 7499940 2398900 357435

Links

Crossrefs

Cf. A007107 (diagonal?), A001501 (row sums), A007105 (column 0?), A110040 (symmetric matrices).

Extensions

More terms from Alois P. Heinz, Apr 09 2017

A284991 Triangle T(n,t) read by rows: the number of n X n {0,1} matrices with trace t where each row sum and each column sum is 4.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 10, 20, 45, 44, 265, 1920, 6300, 13720, 20175, 18000, 7570, 357435, 2398900, 7499940, 14372820, 18433415, 15729000, 8171730, 1975560, 749649145, 4695264000, 13718863480, 24545693760, 29544855480, 24545693760, 13718863480, 4695264000, 749649145
Offset: 0

Views

Author

R. J. Mathar, Apr 07 2017

Keywords

Examples

			0:       1
1:       0       0
2:       0       0       0
3:       0       0       0        0
4:       0       0       0        0        1
5:       1       0      10       20       45       44
6:     265    1920    6300    13720    20175    18000    7570
7:  357435 2398900 7499940 14372820 18433415 15729000 8171730 1975560

Links

Crossrefs

Cf. A058528 (row sums), A007105 (diagonal?), A139670 (symmetric matrices).

Extensions

More terms from Alois P. Heinz, Apr 09 2017

A364068 Triangle T(n,k) read by rows: Number of traceless binary n X n matrices with all row and column sums equal to k, 1<=k<=n.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 9, 9, 1, 0, 44, 216, 44, 1, 0, 265, 7570, 7570, 265, 1, 0, 1854, 357435, 1975560, 357435, 1854, 1, 0, 14833, 22040361, 749649145, 749649145, 22040361, 14833, 1, 0, 133496, 1721632024
Offset: 1

Views

Author

R. J. Mathar, Jul 04 2023

Keywords

Examples

			    0
    1        0
    2        1         0
    9        9         1      0
   44      216        44      1    0
  265     7570      7570    265    1 0
 1854   357435   1975560 357435 1854 1 0
14833 22040361 749649145

Crossrefs

Cf. A000166 (k=1), A007107 (k=2), A284989 (see 1st col), A284990 (see 1st col, k=3), A007105 (k=3?), A284991 (see 1st col, k=4), A008300 (any trace)

Formula

T(n,n)=0. (k=n would require a 1 on the diagonal)
T(n,n-1)=1. (1 at all entries but the diagonal)
T(n,n-k) = T(n,k-1). (Flip entries 0<->1 and erase diagonal) - R. J. Mathar, Jul 26 2023
Showing 1-3 of 3 results.

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

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