A279709 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 1, 2, 1, 2, 4, 2, 3, 5, 8, 3, 4, 11, 13, 16, 5, 6, 22, 42, 34, 32, 8, 9, 47, 125, 161, 89, 64, 13, 14, 102, 385, 717, 617, 233, 128, 21, 22, 224, 1195, 3245, 4121, 2364, 610, 256, 34, 35, 494, 3751, 14988, 27346, 23690, 9057, 1597, 512, 55, 56, 1089, 11823, 70220

Offset: 1

Author

R. H. Hardin, Dec 17 2016

Keywords

• nonn
• tabl

Examples

			Table starts
...1....1......1.......2.........3..........5............8............13
...2....2......3.......4.........6..........9...........14............22
...4....5.....11......22........47........102..........224...........494
...8...13.....42.....125.......385.......1195.........3751.........11823
..16...34....161.....717......3245......14988........70220........329692
..32...89....617....4121.....27346.....187484......1302321.......9047660
..64..233...2364...23690....230128....2342179.....24137862.....248664928
.128..610...9057..136181...1936687...29270275....447547408....6837220721
.256.1597..34699..782826..16300179..365809911...8297886949..187983779265
.512.4181.132938.4500021.137192011.4571688626.153848240903.5168463666199
Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..0..1..0. .0..1..1..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
..1..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..0..1. .0..0..0..1
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .1..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..221

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A001519.

Row 1 is A000045(n-1).

Row 2 is A001611.

Formula

Empirical for column k:

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

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

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

k=4: [order 8] for n>9

k=5: [order 12] for n>13

k=6: [order 32] for n>33

k=7: [order 60] for n>62

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-3)

n=3: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -a(n-5) -a(n-7) -a(n-8)

n=4: [order 23] for n>25

n=5: [order 56] for n>64