A183632 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 4.

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

R. H. Hardin, Table of n, a(n) for n = 1..219

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

Adjacent sequences: A183629 A183630 A183631 * A183633 A183634 A183635

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2011

Status

approved