A281715 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 1, 2, 1, 3, 4, 2, 7, 4, 8, 3, 14, 8, 6, 16, 5, 29, 38, 14, 9, 32, 8, 61, 90, 97, 17, 14, 64, 13, 126, 305, 294, 245, 22, 22, 128, 21, 265, 902, 1410, 937, 631, 30, 35, 256, 34, 553, 2710, 5781, 6417, 3166, 1625, 43, 56, 512, 55, 1162, 8376, 23798, 37781, 29849, 10738, 4234

Offset: 1

Author

R. H. Hardin, Jan 28 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

...2..3..7....14.....29.......61.......126.........265..........553

...4..4..8....38.....90......305.......902........2710.........8376

...8..6.14....97....294.....1410......5781.......23798.......103034

..16..9.17...245....937.....6417.....37781......214045......1321909

..32.14.22...631...3166....29849....252867.....1987696.....17241122

..64.22.30..1625..10738...142023...1721319....18779855....230037168

.128.35.43..4234..37285...677045..11737418...178547832...3076165855

.256.56.64.11017.129586..3244671..80326035..1704685390..41247350230

.512.90.98.28652.452042.15605137.550174620.16297041786.554236736742

Examples

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

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A001611(n+1).

Row 1 is A000045(n-1).

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: a(n) = 2*a(n-1) -a(n-3) for n>6

k=4: [order 15] for n>16

k=5: [order 24] for n>28

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5)

n=3: [order 20] for n>21

n=4: [order 72] for n>73