A281988 T(n,k)=Number of nXk 0..1 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 16, 121, 16, 0, 0, 88, 1054, 1054, 88, 0, 0, 432, 7053, 10852, 7053, 432, 0, 0, 2008, 41118, 89414, 89414, 41118, 2008, 0, 0, 8992, 226025, 659508, 938730, 659508, 226025, 8992, 0, 0, 39200, 1189600, 4668914, 8777256, 8777256

Offset

1,8

Comments

Table starts

.0......0........0..........0...........0.............0..............0

.0......0........2.........16..........88...........432...........2008

.0......2......121.......1054........7053.........41118.........226025

.0.....16.....1054......10852.......89414........659508........4668914

.0.....88.....7053......89414......938730.......8777256.......77613062

.0....432....41118.....659508.....8777256.....104671608.....1170765416

.0...2008...226025....4668914....77613062....1170765416....16521306352

.0...8992..1189600...31829068...662453196...12655050072...225583845888

.0..39200..6090935..212313306..5524744676..133501129836..3008079936046

.0.167552.30538028.1390961304.45282954978.1383406166720.39403294497598

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) =

k=2: a(n) = 8*a(n-1) -20*a(n-2) +24*a(n-3) -36*a(n-4) +16*a(n-5) -16*a(n-6)

k=3: [order 20] for n>23

k=4: [order 56] for n>63

Example

Some solutions for n=4 k=4
..0..1..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..1..1..0. .0..0..0..1. .0..1..1..1. .0..0..0..1. .1..1..1..0
..0..0..1..1. .1..0..1..0. .0..1..1..0. .1..0..0..0. .0..0..0..1
..0..1..0..0. .1..0..1..0. .1..1..0..1. .0..1..1..1. .1..0..0..1

Crossrefs

Sequence in context: A353254 A281034 A282441 * A190389 A285485 A176127

Adjacent sequences: A281985 A281986 A281987 * A281989 A281990 A281991

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 04 2017

Status

approved