A252811 T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every consecutive three elements in every row and column not having exactly two distinct values, and in every diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order

61, 155, 155, 357, 259, 357, 752, 488, 488, 752, 1808, 369, 1337, 369, 1808, 4045, 702, 551, 551, 702, 4045, 8513, 2301, 2068, 742, 2068, 2301, 8513, 19432, 1864, 6961, 1625, 1625, 6961, 1864, 19432, 42308, 3971, 2891, 2795, 3186, 2795, 2891, 3971, 42308

Offset

1,1

Comments

Table starts

....61...155...357...752..1808...4045..8513..19432..42308..88615.195983..419484

...155...259...488...369...702...2301..1864...3971..13398..11033..23486...78603

...357...488..1337...551..2068...6961..2891..10687..35835..15328..56023..186554

...752...369...551...742..1625...2795..3763...8275..14320..19355..42636...73806

..1808...702..2068..1625..3186...9869..7897..15217..46089..37348..72215..218508

..4045..2301..6961..2795..9869..30949.13010..45797.138103..59021.201153..603059

..8513..1864..2891..3763..7897..13010.17895..36732..58811..78891.160955..259629

.19432..3971.10687..8275.15217..45797.36732..69935.206185.164273.299025..854263

.42308.13398.35835.14320.46089.138103.58811.206185.626266.265685.899078.2570383

.88615.11033.15328.19355.37348..59021.78891.164273.265685.365400.722799.1111091

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

k=1: [linear recurrence of order 12] for n>14

k=2: [order 10] for n>16

k=3: [order 16] for n>19

k=4: a(n) = 6*a(n-3) -4*a(n-6) -2*a(n-9) +a(n-12) for n>15

k=5: [order 30] for n>34

k=6: [order 40] for n>46

k=7: [order 34] for n>39

Example

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

Crossrefs

Sequence in context: A305172 A316760 A211333 * A252804 A257746 A062661

Adjacent sequences: A252808 A252809 A252810 * A252812 A252813 A252814

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2014

Status

approved