|
%I #8 Sep 05 2018 08:26:18
%S 4,12,33,78,162,304,527,858,1328,1972,2829,3942,5358,7128,9307,11954,
%T 15132,18908,23353,28542,34554,41472,49383,58378,68552,80004,92837,
%U 107158,123078,140712,160179,181602,205108,230828,258897,289454,322642
%N Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than a single 1 has rows and columns in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A225894/b225894.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/6)*n^4 + (1/6)*n^3 + (4/3)*n^2 + (1/3)*n + 2.
%F Conjectures from _Colin Barker_, Sep 05 2018: (Start)
%F G.f.: x*(4 - 8*x + 13*x^2 - 7*x^3 + 2*x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=3:
%e ..0..0....0..0....0..0....0..1....0..1....0..0....0..0....0..0....0..1....0..1
%e ..1..1....0..0....0..0....1..1....0..0....1..0....0..1....0..1....1..1....1..0
%e ..1..1....1..0....0..0....0..1....1..1....1..1....1..0....0..1....1..1....0..0
%Y Column 2 of A225900.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 20 2013
|
