A253490 - OEIS

%I #10 Dec 15 2018 16:00:48

%S 1388,3090,4196,6931,13528,29370,68992,172050,449608,1219050,3400912,

%T 9693570,28065688,82170330,242460832,719285490,2141665768,6392619210,

%U 19113104752,57209811810,171370433848,513593301690,1539743908672

%N Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

%H R. H. Hardin, <a href="/A253490/b253490.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>7.

%F Empirical: a(n) = 49*3^(n-1) + 494*2^(n-1) + 1655 for n>4.

%F Conjectures from _Colin Barker_, Dec 15 2018: (Start)

%F G.f.: x*(1388 - 5238*x + 924*x^2 + 7417*x^3 - 442*x^4 - 733*x^5 - 6*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

%F a(n) = 1655 + 247*2^n + 49*3^(n-1) for n>4.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A253495.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2015