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