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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A016116(n+1)

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

Sequence in context: A105681 A368548 A375783 * A369902 A130127 A366771

Adjacent sequences: A240036 A240037 A240038 * A240040 A240041 A240042

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 31 2014

Status

approved