# [seqfan] nXk sums of pairs of neighbor values = {0..number of neighbors} ?

Ron Hardin rhhardin at att.net
Wed Dec 28 00:41:09 CET 2011

```https://oeis.org/A203022 . These are difficult to enumerate but examples are
interesting to look at, here 3X3 for all values in 0..11, in a where's Waldo
sort of way.

T(n,k)=Number of nXk nonnegative integer arrays with adjacent horizontal and
vertical element pair sums equal to all values in 0..2nk-n-k-1 (each exactly
once)
Table starts
...0......1........2.........4.......12.....44......176.768
...1......8.......36.......544....12700.431432.17482140....
...2.....36.....3216....257664.69822004....................
...4....544...257664.464458656.............................
..12..12700.69822004.......................................
..44.431432................................................
.176.......................................................
Some solutions for n=3 k=3
..4..5..6....0..3..1....0..2..7....7..3..6....1..5..6....1..0..0....8..2..4..
..1..3..4....0..7..4....0..1..4....0..1..5....1..0..4....9..2..6....1..0..0..
..0..0..2....1..1..5....4..6..2....0..2..3....8..0..3....0..3..1....4..3..8..

rhhardin at mindspring.com
rhhardin at att.net (either)

```