A250625 - OEIS

%I #8 Nov 15 2018 11:07:45

%S 36,125,380,1072,2856,7307,18131,43966,104755,246252,572894,1322172,

%T 3032579,6922433,15743520,35703349,80791394,182511840,411772666,

%U 928103255,2090301223,4705147230,10586418861,23811245592,53543550752

%N Number of (n+1) X (1+1) 0..2 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%H R. H. Hardin, <a href="/A250625/b250625.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + a(n-3) + 16*a(n-4) - 10*a(n-5) - 7*a(n-6) + 6*a(n-7) + a(n-8) - a(n-9).

%F Empirical g.f.: x*(36 - 91*x + 26*x^2 + 131*x^3 - 97*x^4 - 57*x^5 + 55*x^6 + 8*x^7 - 9*x^8) / ((1 - x)^2*(1 - x - x^2)^2*(1 - 2*x - x^2 + x^3)). - _Colin Barker_, Nov 15 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A250632.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014