A253500 - OEIS

%I #8 Dec 16 2018 08:36:01

%S 19701,22236,29370,40117,63550,113573,220988,457436,995132,2264924,

%T 5387708,13382876,34622012,92846684,256535228,725629916,2088972092,

%U 6091114844,17921775548,53062222556,157780493372,470529165404

%N Number of (6+1) X (n+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="/A253500/b253500.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) = 400*3^(n-3) + 2682*2^(n-1) + 16940 for n>6.

%F Empirical g.f.: x*(19701 - 95970*x + 112665*x^2 - 9713*x^3 + 12502*x^4 - 2660*x^5 - 2102*x^6 - 489*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Dec 16 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

%Y Row 6 of A253495.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2015