A222894 T(n,k)=Number of nXk 0..7 arrays with no element equal to another at a city block distance of exactly two, and new values 0..7 introduced in row major order

1, 2, 2, 3, 7, 3, 7, 34, 34, 7, 20, 389, 991, 389, 20, 67, 7145, 84521, 84521, 7145, 67, 255, 179465, 11047723, 46407465, 11047723, 179465, 255, 1080, 5426201, 1639681049, 30122054696, 30122054696, 1639681049, 5426201, 1080, 5016, 180390761

Offset

1,2

Comments

Table starts

....1.........2............3..............7.............20.............67

....2.........7...........34............389...........7145.........179465

....3........34..........991..........84521.......11047723.....1639681049

....7.......389........84521.......46407465....30122054696.20029573364121

...20......7145.....11047723....30122054696.86240147780852

...67....179465...1639681049.20029573364121

..255...5426201.251412693667

.1080.180390761

.5016

Links

R. H. Hardin, Table of n, a(n) for n = 1..49

Formula

Empirical for column k:

k=1: a(n) = 22*a(n-1) -190*a(n-2) +820*a(n-3) -1849*a(n-4) +2038*a(n-5) -840*a(n-6) for n>8

k=2: a(n) = 66*a(n-1) -1353*a(n-2) +10648*a(n-3) -30096*a(n-4) +20736*a(n-5) for n>7

k=3: a(n) = 211*a(n-1) -9385*a(n-2) +110913*a(n-3) -253890*a(n-4) for n>6

Example

Some solutions for n=3 k=4
..0..1..2..2....0..1..2..3....0..1..2..3....0..1..2..3....0..1..1..2
..3..4..5..3....2..4..4..5....4..1..5..6....4..5..5..1....2..3..4..4
..5..2..1..4....6..0..0..2....2..3..0..6....6..3..4..0....5..5..6..7

Crossrefs

Sequence in context: A222944 A222871 A222779 * A210753 A208762 A209746

Adjacent sequences: A222891 A222892 A222893 * A222895 A222896 A222897

Keyword

nonn,tabl

Author

R. H. Hardin Mar 08 2013

Status

approved