A267783 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.

8, 64, 216, 729, 1728, 4096, 8000, 15625, 27000, 46656, 74088, 117649, 175616, 262144, 373248, 531441, 729000, 1000000, 1331000, 1771561, 2299968, 2985984, 3796416, 4826809, 6028568, 7529536, 9261000, 11390625, 13824000, 16777216

Offset: 1

Author

R. H. Hardin, Jan 20 2016

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..0..1....0..0..0....0..1..1....0..0..0....0..0..0....0..0..0....1..1..0
..1..0..0....1..0..1....0..1..0....1..1..0....1..1..0....1..0..1....1..0..1
..1..1..1....1..1..1....1..0..1....0..1..1....1..1..1....1..1..0....0..1..1
..0..0..0....0..0..0....0..1..0....0..0..0....0..0..1....0..0..1....1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 3 of A267788.

Formula

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).

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