A252384 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 7

578, 897, 540, 1359, 555, 588, 1966, 647, 529, 651, 3020, 771, 632, 570, 785, 4682, 1067, 663, 616, 637, 904, 7109, 1496, 963, 744, 799, 764, 1051, 10880, 1928, 1341, 1091, 916, 984, 903, 1290, 16510, 2662, 1610, 1475, 1305, 1097, 1114, 1117, 1543

Offset

1,1

Comments

Table starts

..578..897.1359.1966.3020.4682.7109.10880.16510.24980.37998.57542.86746.131187

..540..555..647..771.1067.1496.1928..2662..3856..5074..7024.10213.13505..18776

..588..529..632..663..963.1341.1610..2376..3331..4097..6077..8560.10605..15764

..651..570..616..744.1091.1475.1880..2734..3712..4817..7023..9576.12499..18249

..785..637..799..916.1305.1894.2310..3280..4791..5934..8451.12386.15413..21987

..904..764..984.1097.1667.2356.2769..4222..5992..7136.10911.15524.18561..28419

.1051..903.1114.1361.2031.2778.3495..5195..7123..9045.13466.18506.23568..35117

.1290.1117.1541.1791.2598.3836.4601..6665..9875.11932.17313.25696.31116..45188

.1543.1470.2007.2270.3526.5035.5840..9089.13006.15176.23653.33887.39610..61778

.1902.1843.2417.2976.4492.6189.7723.11638.16053.20114.30334.41885.52547..79278

Links

R. H. Hardin, Table of n, a(n) for n = 1..579

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-3) -8*a(n-6) +5*a(n-9) -a(n-12) for n>22

k=2: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>15

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

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

k=5: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>12

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

k=7: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>12

Empirical for row n:

n=1: [linear recurrence of order 65] for n>79

n=2: [order 21] for n>30

n=3: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>17

n=4: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>14

n=5: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>14

n=6: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>15

n=7: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>14

Example

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

Crossrefs

Sequence in context: A252376 A031522 A234500 * A252385 A158369 A366067

Adjacent sequences: A252381 A252382 A252383 * A252385 A252386 A252387

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2014

Status

approved