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

Author

R. H. Hardin Mar 06 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A052919(n-2)

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