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%I #16 Dec 27 2023 17:30:21
%S 1,2,4,7,12,19,29,42,59,80,106,137,174,217,267,324,389,462,544,635,
%T 736,847,969,1102,1247,1404,1574,1757,1954,2165,2391,2632,2889,3162,
%U 3452,3759,4084,4427,4789,5170,5571,5992,6434,6897,7382,7889,8419,8972,9549,10150
%N Number of n X 2 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%H Alois P. Heinz, <a href="/A266464/b266464.txt">Table of n, a(n) for n = 0..10000</a> (terms n=1..210 from R. H. Hardin)
%F a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) -a(n-5).
%F From _Colin Barker_, Mar 21 2018: (Start)
%F G.f.: (x^3-x+1)/((x+1)*(x-1)^4).
%F a(n) = (2*n^3 + 3*n^2 + 22*n + 24) / 24 for n even.
%F a(n) = (2*n^3 + 3*n^2 + 22*n + 21) / 24 for n odd.
%F (End)
%e Some solutions for n=4:
%e ..0..0....0..0....0..1....0..0....0..1....0..0....1..1....0..1....0..0....0..1
%e ..0..0....0..0....0..1....1..1....1..0....0..0....1..1....1..0....0..0....1..0
%e ..0..1....0..0....1..0....1..1....1..1....1..1....1..1....1..0....0..0....1..0
%e ..1..0....1..1....1..0....1..1....1..1....1..1....1..1....1..1....0..0....1..0
%p a:= proc(n) option remember;
%p `if`(n<0, 0, 1+a(n-1)+floor(n^2/4))
%p end:
%p seq(a(n), n=0..100); # _Alois P. Heinz_, Dec 27 2023
%Y Column 2 of A266470.
%Y Partial sums of A033638.
%K nonn,easy
%O 0,2
%A _R. H. Hardin_, Dec 29 2015
%E a(0)=1 prepended by _Alois P. Heinz_, Dec 27 2023
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