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A266464 Number of n X 2 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

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