login
Number of (n+1) X (4+1) 0..1 arrays with nondecreasing min(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.
1

%I #8 Nov 20 2018 09:54:52

%S 118,376,1190,3776,12062,38676,124366,400616,1292134,4171276,13474406,

%T 43546448,140781326,455247108,1472416318,4762930232,15408574198,

%U 49852141564,161298304598,521908159904,1688775756830,5464620624372

%N Number of (n+1) X (4+1) 0..1 arrays with nondecreasing min(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="/A250793/b250793.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 8*a(n-3) + 33*a(n-4) - 36*a(n-5) + 8*a(n-7).

%F Empirical g.f.: 2*x*(59 - 284*x + 271*x^2 + 416*x^3 - 624*x^4 + 10*x^5 + 128*x^6) / ((1 - x)^2*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 4*x^2)). - _Colin Barker_, Nov 20 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A250797.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014