A252961 T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order

60, 119, 140, 223, 120, 297, 603, 155, 185, 711, 1251, 249, 259, 337, 1543, 3465, 385, 369, 443, 596, 3461, 7495, 651, 605, 674, 871, 1186, 7637, 20977, 1069, 985, 1027, 1242, 1681, 2279, 16689, 46641, 1757, 1429, 1551, 1747, 2201, 2999, 4165, 35609

Offset

1,1

Comments

Table starts

....60...119...223...603..1251..3465..7495..20977..46641.130201.295421.819671

...140...120...155...249...385...651..1069...1757...2949...5045...8293..14403

...297...185...259...369...605...985..1429...2421...3907...6027...9989..16623

...711...337...443...674..1027..1551..2349...3759...5739...9054..14527..22950

..1543...596...871..1242..1747..2822..4019...6133...9681..14784..22631..37118

..3461..1186..1681..2201..3315..5100..6855..10888..16745..24270..38635..61564

..7637..2279..2999..4275..6091..8767.12573..19192..27929..42791..65583.101848

.16689..4165..6103..8202.11027.16909.23471..33929..52191..76861.115015.182359

.35609..8552.11983.15026.21661.32096.42337..64393..96273.137384.210821.330363

.78429.16744.21749.29799.41149.57282.81323.118916.171809.254784.384825.580538

Links

R. H. Hardin, Table of n, a(n) for n = 1..231

Formula

Empirical for column k:

k=1: [linear recurrence of order 12] for n>15

k=2: [order 12] for n>14

k=3: [order 8] for n>10

k=4: [order 15] for n>17

k=5: [order 14] for n>16

k=6: [order 12] for n>15

k=7: [order 22] for n>25

Empirical for row n:

n=1: [linear recurrence of order 14] for n>16

n=2: [order 9] for n>12

n=3: [order 13] for n>15

n=4: [order 14] for n>16

n=5: [order 17] for n>19

n=6: [order 19] for n>21

n=7: [order 23] for n>25

Example

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

Crossrefs

Sequence in context: A182683 A174601 A306908 * A252962 A296767 A336442

Adjacent sequences: A252958 A252959 A252960 * A252962 A252963 A252964

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2014

Status

approved