%I #13 Jun 05 2022 08:25:30
%S 1,1,5,42,641,14751,478711,20758650,1158207312,80758709676,
%T 6877184737416,701994697409136,84574042067524470,11870290445670605262,
%U 1919446717950100963626,354168049679464581788796,73947210994621695613727526,17342441149450781813176059990
%N Number of (4*n) X n binary arrays with rows in nonincreasing order, 4 ones in every column and no more than 2 ones in any row.
%C Number of n X n symmetric matrices with nonnegative integer entries and all row and column sums 4. - _Andrew Howroyd_, Apr 07 2020
%C In A005816 matrix elements on the diagonal are counted with a factor 2. This sequence here counts labeled multigraphs with n nodes (may be disconnected, undirected edges) without loops and degree at each node <=4. - _R. J. Mathar_, Jun 05 2022
%H Andrew Howroyd, <a href="/A188405/b188405.txt">Table of n, a(n) for n = 0..50</a>
%e All solutions for 8X2
%e ..1..1....1..1....1..1....1..0....1..1
%e ..1..0....1..1....1..1....1..0....1..1
%e ..1..0....1..1....1..0....1..0....1..1
%e ..1..0....1..0....1..0....1..0....1..1
%e ..0..1....0..1....0..1....0..1....0..0
%e ..0..1....0..0....0..1....0..1....0..0
%e ..0..1....0..0....0..0....0..1....0..0
%e ..0..0....0..0....0..0....0..1....0..0
%Y Row 4 of A188403.
%Y Cf. A139670 (matrix elements 0 or 1).
%K nonn
%O 0,3
%A _R. H. Hardin_, Mar 30 2011
%E a(0)=1 prepended and terms a(12) and beyond from _Andrew Howroyd_, Apr 07 2020