A232335 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal

1, 2, 1, 4, 6, 1, 6, 18, 16, 1, 10, 32, 74, 42, 1, 16, 82, 154, 308, 110, 1, 26, 162, 628, 734, 1282, 288, 1, 42, 388, 1470, 4906, 3472, 5338, 754, 1, 68, 806, 5530, 13170, 38986, 16338, 22228, 1974, 1, 110, 1858, 13906, 82526, 117690, 312276, 76630, 92562, 5168

Offset

1,2

Comments

Table starts

.1.....2.......4.......6.........10.........16............26............42

.1.....6......18......32.........82........162...........388...........806

.1....16......74.....154........628.......1470..........5530.........13906

.1....42.....308.....734.......4906......13170.........82526........239992

.1...110....1282....3472......38986.....117690.......1274656.......4158066

.1...288....5338...16338.....312276....1047700......20052758......71916112

.1...754...22228...76630....2510674....9298730.....318521414....1241196022

.1..1974...92562..358656...20221026...82332898....5084744564...21383016966

.1..5168..385450.1676330..162993780..727588212...81376107850..367791626696

.1.13530.1605108.7828014.1314329242.6419787202.1303994749578.6317140944234

Links

R. H. Hardin, Table of n, a(n) for n = 1..448

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)

k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)

k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5

k=6: [order 7] for n>9

k=7: [order 16] for n>18

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2) for n>3

n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6

n=3: [order 8] for n>12

n=4: [order 21] for n>24

n=5: [order 36] for n>42

n=6: [order 80] for n>87

Example

Some solutions for n=5 k=4
..2..1..0..1....2..1..2..1....2..1..0..2....1..2..0..2....2..1..0..1
..0..1..2..0....0..1..2..0....0..2..1..0....0..1..0..1....2..1..2..1
..2..0..1..0....2..0..1..0....1..2..1..0....2..1..2..1....2..1..0..2
..1..2..1..2....1..2..1..2....1..2..1..0....0..1..0..2....0..2..1..2
..1..0..1..0....1..2..1..0....1..0..2..1....2..1..0..2....1..0..1..2

Crossrefs

Column 2 is A025169(n-1)

Column 3 is A218059

Row 1 is A006355(n+1)

Sequence in context: A369518 A199530 A208765 * A098473 A121757 A219441

Adjacent sequences: A232332 A232333 A232334 * A232336 A232337 A232338

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2013

Status

approved