A202047 T(n,k)=Number of zero-sum nXk -1..1 arrays with every element unequal to at most two horizontal and vertical neighbors

1, 3, 3, 7, 19, 7, 19, 73, 73, 19, 51, 335, 415, 335, 51, 141, 1593, 2921, 2921, 1593, 141, 393, 7669, 19541, 31753, 19541, 7669, 393, 1107, 37311, 149149, 359017, 359017, 149149, 37311, 1107, 3139, 184335, 1067983, 4188917, 6221993, 4188917, 1067983

Offset

1,2

Comments

Table starts

....1.......3.........7.........19..........51..........141..........393

....3......19........73........335........1593.........7669........37311

....7......73.......415.......2921.......19541.......149149......1067983

...19.....335......2921......31753......359017......4188917.....49553277

...51....1593.....19541.....359017.....6221993....119412837...2229078023

..141....7669....149149....4188917...119412837...3573771563.108356007319

..393...37311...1067983...49553277..2229078023.108356007319

.1107..184335...8193025..594443301.43322352587

.3139..919889..60897081.7206865523

.8953.4620477.469758219

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Example

Some solutions for n=5 k=3
.-1.-1.-1....1..1..1....0.-1.-1....1..0..0...-1.-1..1....1.-1.-1....1..1..0
..0..0.-1...-1.-1..0....1..1..1....1..0..0....1..1.-1...-1.-1..0....1..1..0
..0..0..1...-1.-1..0....1.-1.-1...-1..0..0....1..1.-1....0..0..0...-1.-1..0
..0..0..1....1..1..1....1.-1..0...-1.-1.-1....0..0..0....1..1..0...-1.-1.-1
..1..1..0...-1.-1..0....1.-1..0....0..1..1...-1..0..0...-1..1..1...-1..1..1

Crossrefs

Column 1 is A002426

Sequence in context: A221303 A221378 A221269 * A036574 A174034 A081486

Adjacent sequences: A202044 A202045 A202046 * A202048 A202049 A202050

Keyword

nonn,tabl

Author

R. H. Hardin Dec 10 2011

Status

approved