A240039 T(n,k)=Number of nXk 0..2 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 3.

2, 2, 2, 4, 2, 4, 4, 6, 6, 4, 8, 4, 16, 4, 8, 8, 10, 16, 16, 10, 8, 16, 8, 42, 18, 42, 8, 16, 16, 20, 44, 52, 52, 44, 20, 16, 32, 16, 114, 62, 154, 62, 114, 16, 32, 32, 40, 122, 162, 178, 178, 162, 122, 40, 32, 64, 32, 314, 204, 494, 282, 494, 204, 314, 32, 64, 64, 80, 340, 530, 600

Offset: 1

Author

R. H. Hardin, Mar 31 2014

Keywords

• nonn
• tabl

Comments

Table starts

..2..2...4...4....8....8....16....16....32.....32.....64.....64.....128.....128

..2..2...6...4...10....8....20....16....40.....32.....80.....64.....160.....128

..4..6..16..16...42...44...114...122...314....340....872....950....2432....2658

..4..4..16..18...52...62...162...204...530....672...1736...2198....5706....7202

..8.10..42..52..154..178...494...600..1606...2014...5262...6690...17464...22360

..8..8..44..62..178..282...710..1074..2770...4162..10836..15764...41374...59680

.16.20.114.162..494..710..1976..2884..7958..12074..31824..49078..130758..197208

.16.16.122.204..600.1074..2884..5706.14686..25224..66774.113794..307698..508002

.32.40.314.530.1606.2770..7958.14686.42470..72446.200916.360716..984770.1730698

.32.32.340.672.2014.4162.12074.25224.72446.147092.407954.778294.2194512.4046228

Examples

			Some solutions for n=3 k=4
..2..1..1..2....2..1..2..1....2..1..2..1....1..2..1..2....1..2..1..2
..1..0..0..0....1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0
..1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0....2..0..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..511

Crossrefs

Column 1 is A016116(n+1)

Column 2 is A163888(n-2) for n>3

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-2) for n>5

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

k=4: [order 24] for n>27

k=5: [order 86] for n>89