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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.
2

%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