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

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

R. H. Hardin, Table of n, a(n) for n = 1..312

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

Adjacent sequences: A222835 A222836 A222837 * A222839 A222840 A222841

Keyword

nonn,tabl

Author

R. H. Hardin Mar 06 2013

Status

approved