A139670 - OEIS

%I #27 Mar 03 2024 08:20:09

%S 1,26,820,35150,1944530,133948836,11234051976,1127512146540,

%T 133475706272700,18406586045919060,2925154024273348296,

%U 530686776655470875076,109004840145995702773410,25164525076896596670014400,6486836210471246515195539840,1856264107759263993451053077856

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

%C From _R. J. Mathar_, Apr 07 2017: (Start)

%C 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:

%C 0:    1;

%C 1:    0,     0;

%C 2:    0,     0,     0;

%C 3:    0,     0,     0,     0;

%C 4:    0,     0,     0,     0,     1;

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

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

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

%C (End)

%H Andrew Howroyd, <a href="/A139670/b139670.txt">Table of n, a(n) for n = 4..30</a>

%e a(4) = 1:

%e   1 1 1 1

%e   1 1 1 1

%e   1 1 1 1

%e   1 1 1 1

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

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

%K nonn

%O 4,2

%A _R. H. Hardin_, Jun 12 2008

%E Terms a(13) and beyond from _Andrew Howroyd_, Mar 09 2020