A252228 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock row and column sum 2 3 or 4 and every diagonal and antidiagonal sum not 2 3 or 4

228, 368, 368, 812, 1028, 812, 1442, 3066, 3066, 1442, 2458, 7724, 9566, 7724, 2458, 4738, 22256, 24932, 24932, 22256, 4738, 9922, 70284, 73826, 58334, 73826, 70284, 9922, 20070, 219824, 231254, 160688, 160688, 231254, 219824, 20070, 38774, 675264

Offset

1,1

Comments

Table starts

...228.....368......812.....1442......2458......4738.......9922......20070

...368....1028.....3066.....7724.....22256.....70284.....219824.....675264

...812....3066.....9566....24932.....73826....231254.....718514....2208224

..1442....7724....24932....58334....160688....512822....1619714....4972874

..2458...22256....73826...160688....412514...1339010....4297634...13186856

..4738...70284...231254...512822...1339010...4329476...13842872...42480650

..9922..219824...718514..1619714...4297634..13842872...44099648..135348914

.20070..675264..2208224..4972874..13186856..42480650..135348914..415405634

.38774.2072804..6786900.15236172..40282992.129860460..414030384.1270689408

.75106.6383492.20903022.46914228.123998850.399765942.1274652450.3911991552

Links

R. H. Hardin, Table of n, a(n) for n = 1..2243

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) +3*a(n-4) -2*a(n-5) -2*a(n-7) for n>10

k=2: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) -a(n-5) -a(n-6) for n>9

k=3: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) -a(n-5) -a(n-6) for n>8

k=4: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) -a(n-5) -a(n-6) for n>8

k=5: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) -a(n-5) -a(n-6) for n>8

k=6: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) -a(n-5) -a(n-6) for n>8

k=7: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) -a(n-5) -a(n-6) for n>8

Example

Some solutions for n=4 k=4
..1..0..2..0..1..1....0..1..1..2..1..1....1..2..0..2..0..2....1..1..0..2..0..1
..1..2..0..2..0..1....2..0..2..0..2..0....2..0..2..0..2..0....1..0..2..0..2..0
..2..0..2..0..2..1....0..2..0..2..0..2....1..2..0..2..0..2....1..2..0..2..0..2
..0..2..0..2..0..2....2..0..2..0..2..1....1..0..2..0..2..1....2..0..2..0..2..0
..2..0..2..0..2..0....0..2..0..2..0..1....0..2..0..2..0..1....0..2..0..2..0..2
..1..1..1..2..0..1....1..0..2..0..2..1....2..0..2..0..1..1....1..1..2..0..2..0

Crossrefs

Sequence in context: A305063 A258550 A335269 * A252221 A154519 A128808

Adjacent sequences: A252225 A252226 A252227 * A252229 A252230 A252231

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 15 2014

Status

approved