A253454 - OEIS

%I #7 Dec 13 2018 08:04:37

%S 19701,31630,39463,52912,83003,147332,285681,590963,1287225,2936843,

%T 7007361,17462243,45313545,121840763,337369041,955847123,2755067865,

%U 8040303083,23671154721,70114001603,208543126185,622031667803

%N Number of (n+1) X (6+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

%H R. H. Hardin, <a href="/A253454/b253454.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>9.

%F Empirical: a(n) = 529*3^(n-3) + 3431*2^(n-1) + 23248 for n>6.

%F Empirical g.f.: x*(19701 - 86576*x + 66394*x^2 + 45858*x^3 + 9844*x^4 - 5432*x^5 - 2750*x^6 - 489*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Dec 13 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 6 of A253456.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2015