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A222838
T(n,k)=Number of nXk 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order
6
1, 2, 2, 3, 7, 3, 7, 24, 24, 7, 19, 96, 72, 96, 19, 55, 384, 216, 216, 384, 55, 163, 1536, 648, 600, 648, 1536, 163, 487, 6144, 1944, 1536, 1536, 1944, 6144, 487, 1459, 24576, 5832, 4056, 4032, 4056, 5832, 24576, 1459, 4375, 98304, 17496, 10584, 9600, 9600, 10584
OFFSET
1,2
COMMENTS
Table starts
.....1.......2.......3.......7......19......55.....163......487.....1459
.....2.......7......24......96.....384....1536....6144....24576....98304
.....3......24......72.....216.....648....1944....5832....17496....52488
.....7......96.....216.....600....1536....4056...10584....27744....72600
....19.....384.....648....1536....4032....9600...22848....55296...133824
....55....1536....1944....4056....9600...24576...55296...124416...279936
...163....6144....5832...10584...22848...55296..138240...301056...642048
...487...24576...17496...27744...55296..124416..301056...743424..1572864
..1459...98304...52488...72600..133824..279936..642048..1572864..3833856
..4375..393216..157464..190104..322944..645504.1382400..3250176..7962624
.13123.1572864..472392..497664..779328.1476096.3022848..6690816.15925248
.39367.6291456.1417176.1302936.1881600.3393024.6690816.14155776.31850496
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>4
k=2: a(n) = 4*a(n-1) for n>3
k=3: a(n) = 3*a(n-1) for n>2
k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4
k=5: a(n) = 2*a(n-1) +2*a(n-3) +a(n-4) for n>7
k=6: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3) +4*a(n-4) -4*a(n-5) +2*a(n-6) -6*a(n-7) +a(n-10) for n>14
k=7: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) +4*a(n-5) +a(n-6) -a(n-9) for n>14
EXAMPLE
Some solutions for n=4 k=4
..0..0..1..2....0..1..2..3....0..0..1..2....0..0..1..2....0..1..1..2
..2..2..1..0....2..3..0..0....1..3..3..0....2..3..3..2....2..2..0..3
..1..3..3..0....2..3..1..1....1..2..2..0....1..1..0..0....1..3..0..1
..1..0..2..2....1..0..2..2....0..0..1..3....0..2..2..3....0..3..2..2
CROSSREFS
Column 1 is A052919(n-2)
Sequence in context: A203362 A368219 A183407 * A222944 A222871 A222779
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 06 2013
STATUS
approved