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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 17 12:32 EST 2020. Contains 331996 sequences. (Running on oeis4.)