A252305 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 1 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 1 3 6 or 7

864, 1126, 1048, 1675, 1031, 1303, 2670, 1370, 1168, 1763, 4349, 1992, 1677, 1516, 2587, 7138, 3171, 2287, 2151, 2350, 3681, 12027, 5056, 3902, 3032, 3669, 3476, 5496, 20001, 7625, 6103, 5230, 5117, 5416, 4905, 8599, 33175, 12412, 8650, 8130, 9368

Offset

1,1

Comments

Table starts

...864..1126..1675..2670..4349...7138..12027..20001...33175...56339....94176

..1048..1031..1370..1992..3171...5056...7625..12412...19904...30526....49974

..1303..1168..1677..2287..3902...6103...8650..14935...23660...33855....58675

..1763..1516..2151..3032..5230...8130..11639..20350...31954...45815....80430

..2587..2350..3669..5117..9368..15444..22521..43870...72344..109721...229454

..3681..3476..5416..7489.14515..24076..34279..70643..120328..173799...386803

..5496..4905..7492.10626.20910..33862..48579.104334..172130..244167...588270

..8599..8198.13386.18971.42082..71636.109845.323902..561288..964169..3701102

.12992.12725.20379.28579.66739.117612.172039.548179.1058568.1616919..6650739

.19992.18474.28688.41037.98782.167798.240515.861326.1546722.2208135.10925806

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: [linear recurrence of order 60] for n>72

k=2: a(n) = 11*a(n-3) -42*a(n-6) +64*a(n-9) -32*a(n-12) for n>24

k=3: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>18

k=4: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>18

k=5: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21

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>24

Empirical for row n:

n=2: a(n) = 11*a(n-3) -42*a(n-6) +64*a(n-9) -32*a(n-12) for n>21

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

n=4: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>15

n=5: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21

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

n=7: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>19

Example

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

Crossrefs

Sequence in context: A344287 A252297 A252298 * A252306 A184451 A203662

Adjacent sequences: A252302 A252303 A252304 * A252306 A252307 A252308

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 16 2014

Status

approved