A300175 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 9, 6, 0, 0, 17, 37, 37, 17, 0, 0, 41, 192, 268, 192, 41, 0, 0, 104, 932, 2620, 2620, 932, 104, 0, 0, 261, 4712, 23522, 50419, 23522, 4712, 261, 0, 0, 655, 23795, 223445, 886940, 886940, 223445, 23795, 655, 0, 0, 1646, 120610, 2117743

Offset

1,8

Comments

Table starts

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

.0...1......3........6.........17............41.............104

.0...3......9.......37........192...........932............4712

.0...6.....37......268.......2620.........23522..........223445

.0..17....192.....2620......50419........886940........16262433

.0..41....932....23522.....886940......30129628......1068913988

.0.104...4712...223445...16262433....1068913988.....73267622156

.0.261..23795..2117743..297460457...37795185266...5003777484149

.0.655.120610.20154626.5454615441.1339340557254.342457741960757

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)

k=3: [order 11] for n>13

k=4: [order 25] for n>26

k=5: [order 66] for n>69

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..1..1. .0..0..0..1
..0..1..0..1. .0..1..0..1. .0..1..1..1. .0..0..1..1. .1..0..1..1
..1..0..0..0. .0..0..1..0. .0..0..1..1. .1..1..1..1. .1..1..0..1
..1..1..0..0. .0..0..0..0. .1..0..1..1. .1..0..0..0. .1..0..1..1
..1..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..1

Crossrefs

Column 2 is A297972.

Sequence in context: A298841 A299602 A299554 * A129533 A360849 A155999

Adjacent sequences: A300172 A300173 A300174 * A300176 A300177 A300178

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 27 2018

Status

approved