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A188405 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.

%I A188405 #13 Jun 05 2022 08:25:30
%S A188405 1,1,5,42,641,14751,478711,20758650,1158207312,80758709676,
%T A188405 6877184737416,701994697409136,84574042067524470,11870290445670605262,
%U A188405 1919446717950100963626,354168049679464581788796,73947210994621695613727526,17342441149450781813176059990
%N A188405 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 A188405 Number of n X n symmetric matrices with nonnegative integer entries and all row and column sums 4. - _Andrew Howroyd_, Apr 07 2020
%C A188405 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 A188405 Andrew Howroyd, <a href="/A188405/b188405.txt">Table of n, a(n) for n = 0..50</a>
%e A188405 All solutions for 8X2
%e A188405 ..1..1....1..1....1..1....1..0....1..1
%e A188405 ..1..0....1..1....1..1....1..0....1..1
%e A188405 ..1..0....1..1....1..0....1..0....1..1
%e A188405 ..1..0....1..0....1..0....1..0....1..1
%e A188405 ..0..1....0..1....0..1....0..1....0..0
%e A188405 ..0..1....0..0....0..1....0..1....0..0
%e A188405 ..0..1....0..0....0..0....0..1....0..0
%e A188405 ..0..0....0..0....0..0....0..1....0..0
%Y A188405 Row 4 of A188403.
%Y A188405 Cf. A139670 (matrix elements 0 or 1).
%K A188405 nonn
%O A188405 0,3
%A A188405 _R. H. Hardin_, Mar 30 2011
%E A188405 a(0)=1 prepended and terms a(12) and beyond from _Andrew Howroyd_, Apr 07 2020