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

1,1

Links

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

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

Example

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

Crossrefs

Column 3 of A267788.

Sequence in context: A209651 A207071 A117219 * A207404 A207705 A264060

Adjacent sequences: A267780 A267781 A267782 * A267784 A267785 A267786

Keyword

nonn

Author

R. H. Hardin, Jan 20 2016

Status

approved