A252532 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

750, 730, 595, 621, 337, 460, 719, 341, 334, 535, 778, 462, 466, 426, 546, 932, 706, 626, 610, 676, 649, 1200, 1000, 1120, 790, 1114, 964, 823, 1498, 1468, 1760, 1592, 1676, 1748, 1344, 1036, 1968, 2420, 2404, 2440, 4420, 2504, 2332, 2312, 1328, 2708, 3480

Offset: 1

Author

R. H. Hardin, Dec 18 2014

Keywords

• nonn
• tabl

Comments

Table starts

..750..730..621...719...778....932...1200....1498....1968....2708.....3473

..595..337..341...462...706...1000...1468....2420....3480....5240.....8872

..460..334..466...626..1120...1760...2404....4304....6832....9416....16864

..535..426..610...790..1592...2440...3160....6368....9760...12640....25472

..546..676.1114..1676..4420...7184..11456...31136...50560...83840...232192

..649..964.1748..2504..7136..13184..19232...54656..102272..150656...427520

..823.1344.2332..3160.10720..18656..25280...85760..149248..202240...686080

.1036.2312.4244..6704.30752..54464..91648..433664..763904.1341440..6471680

.1328.3336.6760.10016.49792.101888.153856..760832.1580032.2410496.11886592

.1756.4800.9112.12640.77696.145792.202240.1243136.2332672.3235840.19890176

Examples

			Some solutions for n=4 k=4
..2..2..3..2..2..3....1..1..0..1..1..0....3..2..2..3..2..2....0..2..1..0..1..1
..3..2..2..3..2..2....2..0..0..3..0..0....3..0..3..3..0..3....0..2..0..0..3..3
..3..0..3..3..0..3....1..0..1..1..0..1....2..2..3..2..2..3....1..1..0..1..1..0
..2..2..3..2..2..3....1..1..0..1..1..0....3..2..2..3..2..2....0..1..1..0..1..1
..3..2..2..3..2..2....3..0..0..2..0..0....3..1..3..3..0..3....0..3..0..0..3..0
..0..0..3..3..1..3....1..0..1..1..0..1....2..2..3..2..2..3....1..1..0..1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..612

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-3) -3*a(n-6) -4*a(n-9) +4*a(n-12) for n>23

k=2: a(n) = 6*a(n-3) -8*a(n-6) for n>10

k=3: a(n) = 6*a(n-3) -8*a(n-6) for n>8

k=4: a(n) = 4*a(n-3) for n>5

k=5: a(n) = 12*a(n-3) -32*a(n-6) for n>8

k=6: a(n) = 12*a(n-3) -32*a(n-6) for n>8

k=7: a(n) = 8*a(n-3) for n>5

Empirical for row n:

n=1: a(n) = 4*a(n-3) -3*a(n-6) -4*a(n-9) +4*a(n-12) for n>39

n=2: a(n) = 6*a(n-3) -8*a(n-6) for n>10

n=3: a(n) = 6*a(n-3) -8*a(n-6) for n>8

n=4: a(n) = 4*a(n-3) for n>5

n=5: a(n) = 12*a(n-3) -32*a(n-6) for n>8

n=6: a(n) = 12*a(n-3) -32*a(n-6) for n>8

n=7: a(n) = 8*a(n-3) for n>5