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A229795 Number of 2 X 2 0..n arrays with rows and columns in lexicographically nondecreasing order.

%I A229795 #9 Sep 21 2018 08:46:40
%S A229795 7,29,86,205,421,777,1324,2121,3235,4741,6722,9269,12481,16465,21336,
%T A229795 27217,34239,42541,52270,63581,76637,91609,108676,128025,149851,
%U A229795 174357,201754,232261,266105,303521,344752,390049,439671,493885,552966,617197
%N A229795 Number of 2 X 2 0..n arrays with rows and columns in lexicographically nondecreasing order.
%H A229795 R. H. Hardin, <a href="/A229795/b229795.txt">Table of n, a(n) for n = 1..210</a>
%F A229795 Empirical: a(n) = (1/3)*n^4 + (7/6)*n^3 + (13/6)*n^2 + (7/3)*n + 1.
%F A229795 Conjectures from _Colin Barker_, Sep 21 2018: (Start)
%F A229795 G.f.: x*(7 - 6*x + 11*x^2 - 5*x^3 + x^4) / (1 - x)^5.
%F A229795 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 A229795 (End)
%e A229795 Some solutions for n=2:
%e A229795 ..0..2....1..2....1..1....1..2....0..1....0..0....0..2....1..2....0..0....0..2
%e A229795 ..1..0....2..2....1..1....2..1....1..0....2..2....0..2....2..0....0..1....2..2
%Y A229795 Row 2 of A229794.
%K A229795 nonn
%O A229795 1,1
%A A229795 _R. H. Hardin_, Sep 29 2013