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A250856 Number of (4+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%I A250856 #7 Nov 21 2018 15:01:51
%S A250856 12311,63631,223933,626416,1499679,3204951,6279401,11485528,19866631,
%T A250856 32808359,52106341,80039896,119451823,173834271,247420689,345283856,
%U A250856 473439991,638958943,850080461,1116336544,1448679871,1859618311
%N A250856 Number of (4+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H A250856 R. H. Hardin, <a href="/A250856/b250856.txt">Table of n, a(n) for n = 1..210</a>
%F A250856 Empirical: a(n) = (76/9)*n^6 + (1595/12)*n^5 + (28765/36)*n^4 + (31373/12)*n^3 + (155683/36)*n^2 + (10223/3)*n + 1024.
%F A250856 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250856 G.f.: x*(12311 - 22546*x + 37047*x^2 - 35749*x^3 + 21160*x^4 - 7167*x^5 + 1024*x^6) / (1 - x)^7.
%F A250856 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A250856 (End)
%e A250856 Some solutions for n=2:
%e A250856 ..0..0..0....3..3..1....3..1..0....2..2..2....3..3..3....3..2..1....3..3..3
%e A250856 ..3..3..3....1..1..1....0..0..0....1..1..1....0..0..0....0..0..0....2..3..3
%e A250856 ..1..1..1....2..2..2....0..0..0....1..1..1....0..0..0....2..2..2....1..2..2
%e A250856 ..3..3..3....0..1..1....0..0..0....0..3..3....0..0..0....0..0..0....0..1..1
%e A250856 ..0..0..0....1..2..3....1..2..2....0..3..3....2..2..2....0..0..0....0..1..1
%Y A250856 Row 4 of A250853.
%K A250856 nonn
%O A250856 1,1
%A A250856 _R. H. Hardin_, Nov 28 2014