A280069 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 4, 3, 5, 9, 15, 15, 9, 5, 8, 19, 39, 52, 39, 19, 8, 13, 41, 104, 170, 170, 104, 41, 13, 21, 88, 281, 603, 790, 603, 281, 88, 21, 34, 189, 771, 2157, 3729, 3729, 2157, 771, 189, 34, 55, 406, 2122, 7777, 17468, 23564, 17468, 7777, 2122

Offset: 1

Author

R. H. Hardin, Dec 25 2016

Keywords

• nonn
• tabl

Comments

Table starts

..1...1....1......2.......3........5.........8..........13...........21

..1...1....2......4.......9.......19........41..........88..........189

..1...2....5.....15......39......104.......281.........771.........2122

..2...4...15.....52.....170......603......2157........7777........28195

..3...9...39....170.....790.....3729.....17468.......82769.......394904

..5..19..104....603....3729....23564....145485......915505......5786757

..8..41..281...2157...17468...145485...1188839.....9934415.....83159859

.13..88..771...7777...82769...915505...9934415...110266512...1225662273

.21.189.2122..28195..394904..5786757..83159859..1225662273..18113056960

.34.406.5858.102429.1890877.36671797.698377561.13669391105.268403179093

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..263

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A078039(n-2).

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) for n>3

k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) for n>4

k=3: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) +5*a(n-4) -2*a(n-5) -2*a(n-6) -a(n-7) for n>9

k=4: [order 15] for n>18

k=5: [order 35] for n>40

k=6: [order 87] for n>91