A253452 - OEIS

A253452

Number of (n+1) X (4+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

%I #8 Dec 13 2018 08:07:44

%S 3639,8554,11147,15730,26831,52912,114717,266911,656997,1694263,

%T 4540077,12545551,35498037,102227623,298160637,877448191,2598287877,

%U 7726760983,23044088397,68859886831,206034914517,617015262343,1848866835357

%N Number of (n+1) X (4+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

%H R. H. Hardin, <a href="/A253452/b253452.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) + 1039*2^(n-1) + 5372 for n>6.

%F Empirical g.f.: x*(3639 - 13280*x - 148*x^2 + 21108*x^3 + 3744*x^4 - 1926*x^5 - 1994*x^6 - 345*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 ..1..1..2..1..0....0..0..0..1..1....0..1..2..1..1....1..1..0..2..0

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

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

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

%Y Column 4 of A253456.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2015