A280554 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 0, 0, 1, 9, 9, 1, 2, 34, 50, 34, 2, 6, 87, 144, 144, 87, 6, 13, 194, 325, 382, 325, 194, 13, 29, 400, 670, 832, 832, 670, 400, 29, 60, 790, 1316, 1666, 1764, 1666, 1316, 790, 60, 122, 1511, 2502, 3182, 3438, 3438, 3182, 2502, 1511, 122, 241, 2830, 4654

Offset: 1

Author

R. H. Hardin, Jan 05 2017

Keywords

• nonn
• tabl

Comments

Table starts

...0....0....0.....1.....2.....6....13.....29.....60....122....241....468

...0....0....9....34....87...194...400....790...1511...2830...5213...9484

...0....9...50...144...325...670..1316...2502...4654...8521..15412..27612

...1...34..144...382...832..1666..3182...5886..10680..19122..33920..59754

...2...87..325...832..1764..3438..6386..11506..20389..35757..62317.108150

...6..194..670..1666..3438..6502.11697..20440..35226..60300.102974.175746

..13..400.1316..3182..6386.11697.20334..34360..57389..95548.159360.266756

..29..790.2502..5886.11506.20440.34360..56102..90614.146264.237392.388378

..60.1511.4654.10680.20389.35226.57389..90614.141398.220709.347310.553046

.122.2830.8521.19122.35757.60300.95548.146264.220709.332810.506359.781682

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..391

Crossrefs

Column 1 is A055243(n-4).

Column 2 is A279128.

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>9

k=3: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>10

k=4: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>11

k=5: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12

k=6: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12

k=7: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12