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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
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 31 2014
STATUS
approved