A267783 - OEIS

%I #11 Jan 11 2019 11:48:03

%S 8,64,216,729,1728,4096,8000,15625,27000,46656,74088,117649,175616,

%T 262144,373248,531441,729000,1000000,1331000,1771561,2299968,2985984,

%U 3796416,4826809,6028568,7529536,9261000,11390625,13824000,16777216

%N Number of n X 3 0..1 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.

%H R. H. Hardin, <a href="/A267783/b267783.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12).

%F Empirical g.f.: x*(8 + 48*x + 56*x^2 + 121*x^3 + 86*x^4 + 44*x^5 - 14*x^6 + 6*x^7 + 10*x^8 - 4*x^9 - 2*x^10 + x^11) / ((1 - x)^7*(1 + x)^5). - _Colin Barker_, Jan 11 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A267788.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2016