A200770 - OEIS

%I #14 Oct 14 2025 23:26:09

%S 3,3,2,7,9,6,22,30,20,75,105,70,266,378,252,966,1386,924,3564,5148,

%T 3432,13299,19305,12870,50050,72930,48620,189618,277134,184756,722228,

%U 1058148,705432,2762942,4056234,2704156,10608612,15600900,10400600,40859500,60174900

%N Number of nX1 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%H R. H. Hardin, <a href="/A200770/b200770.txt">Table of n, a(n) for n = 1..210</a>

%F Conjecture: (n+2)*(2770*n-4893)*a(n) + 3*(1090*n^2-4919*n+1654)*a(n-1) + 4686*a(n-2) + 2*(-5540*n^2+7016*n+17127)*a(n-3) - 6*(1090*n-2739)*(2*n-7)*a(n-4) = 0. - _R. J. Mathar_, Nov 23 2011 [corrected by _Jason Yuen_, Oct 14 2025]

%e All solutions for n=4

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

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

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

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

%Y Column 1 of A200777.

%Y Includes A003409((n+1)/3) and A000984(n/3).

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2011