OFFSET
1,1
COMMENTS
Table starts
.......146.......666.......3254.....16626.....87686....473586...2605574
.......666......2442.......9990.....43986....204246....987762...4934070
......3254......9990......35162....135966....563114...2458590..11196842
.....16626.....43986.....135966....469146...1755246...6990906..29275086
.....87686....204246.....563114...1755246...5992826..21960366..85187834
....473586....987762....2458590...6990906..21960366..74549082.269462670
...2605574...4934070...11196842..29275086..85187834.269462670
..14548626..25308786...52793406.127755066.346364046
..82214726.132730326..256308074.577190766
.469200306.709335282.1275989790
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..83
FORMULA
Empirical, for every row and column: a(n)=21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6).
The coefficient of a(n-i) is -s(7,7-i), s() being the Stirling number of the first kind, via D. S. McNeil and M. F. Hasler in the Sequence Fans Mailing List.
For a 0..z array with 2 X 2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i).
EXAMPLE
Some solutions for 4 X 3
..3..3..2....2..4..3....4..1..5....2..1..4....4..3..2....2..3..2....3..1..3
..0..4..1....4..0..3....2..3..1....5..2..3....3..0..5....5..0..5....4..2..4
..5..1..4....4..2..5....4..1..5....3..0..5....3..4..1....1..4..1....3..1..3
..2..2..3....1..3..0....3..2..2....5..2..3....1..2..3....4..1..4....1..5..1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 06 2011
STATUS
approved