A250762 - OEIS

%I #10 Nov 18 2018 09:45:34

%S 29012,67356,121593,191723,277746,379662,497471,631173,780768,946256,

%T 1127637,1324911,1538078,1767138,2012091,2272937,2549676,2842308,

%U 3150833,3475251,3815562,4171766,4543863,4931853,5335736,5755512,6191181,6642743

%N Number of (7+1) X (n+1) 0..2 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="/A250762/b250762.txt">Table of n, a(n) for n = 1..134</a>

%F Empirical: a(n) = (15893/2)*n^2 + (29009/2)*n + 6561.

%F Conjectures from _Colin Barker_, Nov 18 2018: (Start)

%F G.f.: x*(29012 - 19680*x + 6561*x^2) / (1 - x)^3.

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

%F (End)

%e Some solutions for n=4:

%e ..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....1..1..1..1..1

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

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

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

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

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

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

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

%Y Row 7 of A250755.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014