A232149 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally, diagonally or antidiagonally

1, 3, 1, 7, 23, 1, 15, 191, 145, 1, 33, 1299, 3669, 887, 1, 73, 9097, 67725, 67311, 5487, 1, 161, 65837, 1345057, 3409361, 1270511, 33957, 1, 355, 474721, 27888353, 191897041, 177194147, 23931701, 210039, 1, 783, 3410799, 572956549, 11346946019

Offset

1,2

Comments

Table starts

.1.......3..........7.............15................33....................73

.1......23........191...........1299..............9097.................65837

.1.....145.......3669..........67725...........1345057..............27888353

.1.....887......67311........3409361.........191897041...........11346946019

.1....5487....1270511......177194147.......28299613241.........4807617578085

.1...33957...23931701.....9181257593.....4162183572673......2029709037695893

.1..210039..450210003...475203378037...611509764410977....855821105743586179

.1.1299219.8472530835.24603676419865.89867078251266793.360977861939388247605

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=2: a(n) = 5*a(n-1) +6*a(n-2) +8*a(n-3) +3*a(n-4) -8*a(n-5) -5*a(n-6)

k=3: [order 9]

k=4: [order 32]

k=5: [order 81]

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-3)

n=2: a(n) = 6*a(n-1) +4*a(n-2) +25*a(n-3) +60*a(n-4) -24*a(n-5) -72*a(n-6)

n=3: [order 19]

n=4: [order 58]

Example

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

Crossrefs

Row 1 is A193641

Sequence in context: A036575 A347485 A073676 * A348115 A282422 A282685

Adjacent sequences: A232146 A232147 A232148 * A232150 A232151 A232152

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2013

Status

approved