A222944 T(n,k) = Number of n X k 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.

1, 2, 2, 3, 7, 3, 7, 33, 33, 7, 20, 273, 420, 273, 20, 66, 2433, 5880, 5880, 2433, 66, 238, 21873, 82320, 130680, 82320, 21873, 238, 902, 196833, 1152480, 2883000, 2883000, 1152480, 196833, 902, 3510, 1771473, 16134720, 63772920, 100692120, 63772920

Offset

1,2

Comments

Table starts

......1..........2...........3............7............20.............66

......2..........7..........33..........273..........2433..........21873

......3.........33.........420.........5880.........82320........1152480

......7........273........5880.......130680.......2883000.......63772920

.....20.......2433.......82320......2883000.....100692120.....3510873720

.....66......21873.....1152480.....63772920....3510873720...194281940280

....238.....196833....16134720...1409319480..122511965400.10720371319680

....902....1771473...225886080..31155452280.4273149243000

...3510...15943233..3162405120.688658403000

..13846..143489073.44273671680

..54998.1291401633

.219222

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3) for n > 5;

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

k=3: a(n) = 14*a(n-1) for n > 3;

k=4: a(n) = 17*a(n-1) +136*a(n-2) -512*a(n-3) for n > 5;

k=5: [order 16 for n > 18].

Example

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

Crossrefs

Sequence in context: A203362 A183407 A222838 * A222871 A222779 A222894

Adjacent sequences: A222941 A222942 A222943 * A222945 A222946 A222947

Keyword

nonn,tabl

Author

R. H. Hardin Mar 09 2013

Status

approved