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A183642 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to 6 10
44, 136, 136, 452, 340, 452, 1576, 952, 952, 1576, 5684, 2884, 2300, 2884, 5684, 21016, 9256, 6136, 6136, 9256, 21016, 79172, 31060, 17612, 14644, 17612, 31060, 79172, 302536, 107992, 53512, 38056, 38056, 53512, 107992, 302536, 1168724, 386404 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
......44.....136.....452....1576.....5684....21016....79172...302536..1168724
.....136.....340.....952....2884.....9256....31060...107992...386404..1415176
.....452.....952....2300....6136....17612....53512...170300...563416..1926572
....1576....2884....6136...14644....38056...105604...309016...945364..3004936
....5684....9256...17612...38056....90524...231736...629132..1793416..5328764
...21016...31060...53512..105604...231736...551380..1398952..3743524.10479256
...79172..107992..170300..309016...629132..1398952..3333500..8411896.22294892
..302536..386404..563416..945364..1793416..3743524..8411896.20077684.50494696
.1168724.1415176.1926572.3004936..5328764.10479256.22294892.50494696
.4552696.5281780.6776872.9877924.16413016.30483700.61632712
LINKS
FORMULA
Empirical, for every row and column: a(n)=10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4)
The coefficient of a(n-i) is -s(5,5-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 2X2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i)
EXAMPLE
Some solutions for 4X3
..2..2..1....1..1..2....1..1..0....2..1..1....1..3..2....3..1..2....2..1..3
..2..0..3....2..2..1....1..3..2....2..1..3....1..1..0....0..2..1....3..0..2
..1..3..0....2..0..3....1..1..0....3..0..2....1..3..2....1..3..0....2..1..3
..1..1..2....3..1..2....1..3..2....1..2..2....1..1..0....2..0..3....1..2..0
CROSSREFS
Sequence in context: A253320 A230829 A358818 * A183634 A043506 A044376
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 06 2011
STATUS
approved

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Last modified June 22 12:48 EDT 2024. Contains 373571 sequences. (Running on oeis4.)