A139670 Number of n X n symmetric binary matrices with all row sums 4.

1, 26, 820, 35150, 1944530, 133948836, 11234051976, 1127512146540, 133475706272700, 18406586045919060, 2925154024273348296, 530686776655470875076, 109004840145995702773410, 25164525076896596670014400, 6486836210471246515195539840, 1856264107759263993451053077856

Offset: 4

Author

R. H. Hardin, Jun 12 2008

Keywords

• nonn

Comments

From R. J. Mathar, Apr 07 2017: (Start)

These are the row sums of the following triangle, which shows in row n and column t the number of symmetric n X n {0,1}-matrices with trace t and 4 ones in each row and each column, 0 <= t <= n:

0: 1;

1: 0, 0;

2: 0, 0, 0;

3: 0, 0, 0, 0;

4: 0, 0, 0, 0, 1;

5: 1, 0, 10, 0, 15, 0;

6: 15, 0, 270, 0, 465, 0, 70;

7: 465, 0, 9660, 0, 19355, 0, 5670, 0;

(End)

Examples

			a(4) = 1:
  1 1 1 1
  1 1 1 1
  1 1 1 1
  1 1 1 1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 4..30

Crossrefs

Column k=4 of A333157 and row 4 of A188448.

Cf. A000085 (row sums 1), A000986 (row sums 2), A110040 (row sums 3).

Extensions

Terms a(13) and beyond from Andrew Howroyd, Mar 09 2020