A250881 - OEIS

%I #7 Nov 22 2018 11:33:48

%S 8736,30360,73122,144248,250964,400496,600070,856912,1178248,1571304,

%T 2043306,2601480,3253052,4005248,4865294,5840416,6937840,8164792,

%U 9528498,11036184,12695076,14512400,16495382,18651248,20987224,23510536,26228410

%N 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 x(i,j)+x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250881/b250881.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (3613/3)*n^3 + 3343*n^2 + (9494/3)*n + 1024.

%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)

%F G.f.: 2*x*(4368 - 2292*x + 2049*x^2 - 512*x^3) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=4:

%e ..2..2..2..2..2....0..0..0..0..0....0..0..0..0..0....2..2..2..2..2

%e ..2..2..2..2..2....3..3..3..3..3....1..1..1..1..1....3..3..3..3..3

%e ..0..0..0..0..0....1..2..2..2..2....3..3..3..3..3....1..1..1..1..1

%e ..0..0..0..1..1....0..1..2..3..3....1..1..1..1..2....3..3..3..3..3

%e ..1..1..1..2..2....0..1..2..3..3....0..0..1..1..2....1..1..3..3..3

%Y Row 4 of A250877.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014