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A183632
T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 4
10
19, 45, 45, 115, 87, 115, 309, 189, 189, 309, 859, 447, 355, 447, 859, 2445, 1125, 741, 741, 1125, 2445, 7075, 2967, 1675, 1383, 1675, 2967, 7075, 20709, 8109, 4029, 2829, 2829, 4029, 8109, 20709, 61099, 22767, 10195, 6207, 5299, 6207, 10195, 22767, 61099
OFFSET
1,1
COMMENTS
Table starts
.....19.....45....115....309....859...2445...7075...20709...61099..181245
.....45.....87....189....447...1125...2967...8109...22767...65205..189447
....115....189....355....741...1675...4029..10195...26901...73435..205869
....309....447....741...1383...2829...6207..14421...35223...89949..238767
....859...1125...1675...2829...5299..10725..23035...52029..123139..304725
...2445...2967...4029...6207..10725..20247..40749...86127..190005..437127
...7075...8109..10195..14421..23035..40749..77635..155781..325195..703389
..20709..22767..26901..35223..52029..86127.155781..299463..599949.1240287
..61099..65205..73435..89949.123139.190005.325195..599949.1162579.2327205
.181245.189447.205869.238767.304725.437127.703389.1240287.2327205.4540407
LINKS
FORMULA
Empirical, for every row and column: a(n)=6*a(n-1)-11*a(n-2)+6*a(n-3)
The coefficient of a(n-i) is -s(4,4-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..0..2....0..1..1....1..1..1....1..1..1....2..0..1....2..0..2....0..2..0
..1..1..1....1..2..0....2..0..2....2..0..2....0..2..1....0..2..0....1..1..1
..2..0..2....1..0..2....2..0..2....0..2..0....1..1..0....2..0..2....0..2..0
..2..0..2....1..2..0....1..1..1....2..0..2....0..2..1....2..0..2....1..1..1
CROSSREFS
Sequence in context: A044096 A044477 A140680 * A359558 A245864 A183624
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 06 2011
STATUS
approved