A250654 - OEIS

A250654

Number of (n+1) X (6+1) 0..1 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.

%I #7 Nov 15 2018 12:50:26

%S 64,134,274,554,1114,2234,4474,8954,17914,35834,71674,143354,286714,

%T 573434,1146874,2293754,4587514,9175034,18350074,36700154,73400314,

%U 146800634,293601274,587202554,1174405114,2348810234,4697620474

%N Number of (n+1) X (6+1) 0..1 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="/A250654/b250654.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*36 + (5*2^(n-1)-1)*6 + 2^(n+1).

%F Empirical g.f.: 2*x*(32 - 29*x) / ((1 - x)*(1 - 2*x)). - _Colin Barker_, Nov 15 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 6 of A250656.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014