A252192 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 1 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 1 3 6 or 7

945, 1440, 1440, 2055, 1886, 2055, 3341, 2610, 2610, 3341, 5300, 3996, 3705, 3996, 5300, 7973, 6368, 5460, 5460, 6368, 7973, 13044, 9508, 8945, 9233, 8945, 9508, 13044, 21238, 15094, 13737, 14130, 14130, 13737, 15094, 21238, 32234, 24092, 20974, 21417

Offset

1,1

Comments

Table starts

...945..1440..2055...3341...5300...7973..13044...21238...32234...53032....87440

..1440..1886..2610...3996...6368...9508..15094...24092...36352...58610....94310

..2055..2610..3705...5460...8945..13737..20974...34209...53194...82196...134418

..3341..3996..5460...9233..14130..21417..34532...55336...84332..135776...218896

..5300..6368..8945..14130..24956..37035..57284...99128..151616..245908...420808

..7973..9508.13737..21417..37035..57629..87230..150297..239980..380896...661172

.13044.15094.20974..34532..57284..87230.147696..246676..385720..640208..1157336

.21238.24092.34209..55336..99128.150297.246676..488200..772384.1382480..3132872

.32234.36352.53194..84332.151616.239980.385720..772384.1339760.2298824..5554000

.53032.58610.82196.135776.245908.380896.640208.1382480.2298824.4201296.12409744

Links

R. H. Hardin, Table of n, a(n) for n = 1..449

Formula

Empirical for column k:

k=1: [linear recurrence of order 24] for n>30

k=2: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>16

k=3: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>15

k=4: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>17

k=5: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>22

k=6: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21

k=7: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>23

Example

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

Crossrefs

Sequence in context: A104438 A125013 A294576 * A252185 A005231 A174865

Adjacent sequences: A252189 A252190 A252191 * A252193 A252194 A252195

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 15 2014

Status

approved