A280161 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 2, 2, 8, 8, 2, 5, 18, 31, 18, 5, 8, 40, 94, 94, 40, 8, 15, 92, 305, 424, 305, 92, 15, 26, 208, 950, 1854, 1854, 950, 208, 26, 46, 470, 2901, 7628, 10677, 7628, 2901, 470, 46, 80, 1060, 8728, 30874, 58852, 58852, 30874, 8728, 1060, 80, 139, 2384, 26068

Offset: 1

Author

R. H. Hardin, Dec 27 2016

Keywords

• nonn
• tabl

Comments

Table starts

..0....0.....2......2.......5.........8.........15..........26...........46

..0....4.....8.....18......40........92........208.........470.........1060

..2....8....31.....94.....305.......950.......2901........8728........26068

..2...18....94....424....1854......7628......30874......123312.......488256

..5...40...305...1854...10677.....58852.....318220.....1695030......8941285

..8...92...950...7628...58852....434790....3138340....22348406....157294986

.15..208..2901..30874..318220...3138340...30089398...285461736...2671391625

.26..470..8728.123312.1695030..22348406..285461736..3612425586..45045404794

.46.1060.26068.488256.8941285.157294986.2671391625.45045404794.748382706193

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 1 is A006367(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>8

k=3: [order 14] for n>19

k=4: [order 30] for n>36

k=5: [order 70] for n>80