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A183662
T(n,k) = Number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock summing to 10.
10
146, 666, 666, 3254, 2442, 3254, 16626, 9990, 9990, 16626, 87686, 43986, 35162, 43986, 87686, 473586, 204246, 135966, 135966, 204246, 473586, 2605574, 987762, 563114, 469146, 563114, 987762, 2605574, 14548626, 4934070, 2458590, 1755246
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
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
Sequence in context: A211838 A158132 A043431 * A183654 A183653 A231243
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 06 2011
STATUS
approved