A279977 T(n,k) is the number of n X k 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 0, 0, 3, 0, 3, 9, 9, 0, 3, 24, 50, 31, 0, 9, 62, 221, 296, 108, 0, 15, 134, 822, 1922, 1650, 366, 0, 31, 277, 2669, 10491, 15511, 8666, 1205, 0, 57, 542, 8068, 50690, 124030, 118857, 43543, 3873, 0, 108, 1035, 23169, 226771, 887491, 1393359, 876704, 211650

Offset: 1

Author

R. H. Hardin, Dec 24 2016

Keywords

• nonn
• tabl

Examples

			Table starts:
.0.....1.......0.........3...........3............9.............15
.0.....3.......9........24..........62..........134............277
.0.....9......50.......221.........822.........2669...........8068
.0....31.....296......1922.......10491........50690.........226771
.0...108....1650.....15511......124030.......887491........5870751
.0...366....8666....118857.....1393359.....14787217......144819856
.0..1205...43543....876704....15071233....237386464.....3444870482
.0..3873..211650...6281773...158391708...3703836674....79672440007
.0.12207.1002602..43997218..1627160233..56499013470..1801951754910
.0.37859.4652327.302544617.16409869901.846166990079.40020022178950
...
Some solutions for n=4 and k=4:
..0..1..0..0. .0..1..0..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
..0..0..1..0. .0..1..1..0. .0..1..0..0. .1..0..1..0. .1..0..1..1
..1..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..0..1. .1..0..1..1
..1..0..0..1. .0..0..1..0. .0..0..0..1. .1..0..0..1. .0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..198

Crossrefs

Row 1 is A105423(n-2).

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 9*a(n-1) -30*a(n-2) +45*a(n-3) -30*a(n-4) +9*a(n-5) -a(n-6)

k=3: [order 9] for n>10

k=4: [order 24]

k=5: [order 38] for n>39

k=6: [order 96] for n>97

Empirical for row n:

n=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

n=2: [order 8] for n>10

n=3: [order 24] for n>30

n=4: [order 68] for n>78