A250903 - OEIS

A250903

Number of (5+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%I #13 Nov 23 2018 21:17:32

%S 4213,15111,44525,119359,305429,764315,1893433,4673299,11537593,

%T 28584535,71295237,179606071,458428429,1188689987,3137057025,

%U 8433329995,23088675409,64300637535,181823356333,520893887439,1508445493253

%N Number of (5+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250903/b250903.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).

%F Empirical g.f.: x*(4213 - 43871*x + 191076*x^2 - 458178*x^3 + 668501*x^4 - 617575*x^5 + 358558*x^6 - 119604*x^7 + 17496*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 23 2018

%e Some solutions for n=4:

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

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

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

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

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

%e 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 1 1 1 1 2

%Y Row 5 of A250898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014