A306136 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 13, 24, 1, 1, 82, 64, 64, 82, 1, 1, 272, 240, 498, 240, 272, 1, 1, 908, 842, 2922, 2922, 842, 908, 1, 1, 3076, 3302, 16877, 31843, 16877, 3302, 3076, 1, 1, 10444, 12740, 111073, 267988, 267988, 111073, 12740, 10444, 1, 1, 35480, 48468

Offset

1,5

Comments

Table starts

.1.....1.....1.......1.........1...........1............1..............1

.1.....4.....8......24........82.........272..........908...........3076

.1.....8....13......64.......240.........842.........3302..........12740

.1....24....64.....498......2922.......16877.......111073.........700859

.1....82...240....2922.....31843......267988......2889140.......29281552

.1...272...842...16877....267988.....3176303.....50158767......730698959

.1...908..3302..111073...2889140....50158767...1284005626....29447872807

.1..3076.12740..700859..29281552...730698959..29447872807..1028875496355

.1.10444.48468.4405884.289967701.10451513277.652802237683.34579655304548

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 20]

k=4: [order 71] for n>72

Example

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

Crossrefs

Column 2 is A303882.

Sequence in context: A316576 A304551 A316376 * A317271 A304419 A316244

Adjacent sequences: A306133 A306134 A306135 * A306137 A306138 A306139

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 22 2018

Status

approved