A240642 T(n,k)=Number of nXk 0..3 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..3 introduced in row major order

1, 1, 1, 2, 5, 2, 5, 27, 27, 5, 14, 193, 462, 193, 14, 41, 1391, 7993, 7993, 1391, 41, 122, 10072, 138882, 333308, 138882, 10072, 122, 365, 72941, 2413198, 13897353, 13897353, 2413198, 72941, 365, 1094, 528283, 41931738, 579476701, 1390560136

Offset

1,4

Comments

Table starts

....1........1............2................5...................14

....1........5...........27..............193.................1391

....2.......27..........462.............7993...............138882

....5......193.........7993...........333308.............13897353

...14.....1391.......138882.........13897353...........1390560136

...41....10072......2413198........579476701.........139138607313

..122....72941.....41931738......24162243789.......13922129807222

..365...528283....728606311....1007486056500.....1393040370960551

.1094..3826157..12660271050...42008844856285...139386826311366370

.3281.27711478.219985006177.1751630302786777.13946966455660995272

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>3

k=2: a(n) = 6*a(n-1) +10*a(n-2) -6*a(n-3) -9*a(n-4) for n>6

k=3: a(n) = 14*a(n-1) +54*a(n-2) +82*a(n-3) -14*a(n-4) -54*a(n-5) -81*a(n-6)

k=4: [order 14]

k=5: [order 31]

Example

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

Crossrefs

Column 1 is A007051(n-2)

Sequence in context: A268789 A269920 A240706 * A240774 A198604 A198253

Adjacent sequences: A240639 A240640 A240641 * A240643 A240644 A240645

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 09 2014

Status

approved