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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 (list; table; graph; refs; listen; history; text; internal format)
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: A220498 A330772 A105681 * A130127 A217982 A184727

Adjacent sequences:  A240036 A240037 A240038 * A240040 A240041 A240042

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 31 2014

STATUS

approved

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Last modified May 27 08:12 EDT 2022. Contains 354096 sequences. (Running on oeis4.)