A250848 - OEIS

%I #10 Nov 21 2018 09:17:47

%S 1225,8037,44797,223933,1043885,4648157,20067117,84805533,353060845,

%T 1454214877,5943685037,24157039133,97778698605,394573711197,

%U 1588686176557,6385947864733,25637459261165,102830957105117

%N Number of (n+1) X (3+1) 0..3 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="/A250848/b250848.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (18104*4^n - 26144*3^n + 10680*2^n - 644)/12.

%F Empirical g.f.: x*(1225 - 4213*x + 7302*x^2 - 3992*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). -_Colin Barker_, Nov 21 2018

%e Some solutions for n=3:

%e ..3..1..1..1....2..2..2..2....3..3..2..3....1..1..0..0....1..1..1..1

%e ..1..1..1..1....1..2..2..3....2..2..2..3....0..0..0..0....1..1..3..3

%e ..1..1..3..3....1..2..2..3....0..1..1..2....2..2..3..3....0..0..2..2

%e ..1..1..3..3....0..1..2..3....0..1..1..3....2..2..3..3....0..1..3..3

%Y Column 3 of A250853.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014