A281139 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one 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, 1, 0, 1, 2, 24, 24, 2, 8, 112, 297, 112, 8, 28, 504, 1046, 1046, 504, 28, 94, 2528, 3460, 2368, 3460, 2528, 94, 304, 11712, 10790, 5368, 5368, 10790, 11712, 304, 960, 52160, 32692, 12064, 9484, 12064, 32692, 52160, 960, 2976, 230048, 96454, 27218

Offset

1,7

Comments

Table starts

....0.......0......1......2......8.....28.....94....304.....960....2976....9096

....0.......0.....24....112....504...2528..11712..52160..230048.1000320.4294016

....1......24....297...1046...3460..10790..32692..96454..279958..801574.2269012

....2.....112...1046...2368...5368..12064..27218..61508..137320..303016..661750

....8.....504...3460...5368...9484..17592..33199..63976..124361..236858..440416

...28....2528..10790..12064..17592..29408..51158..90312..164300..299484..534922

...94...11712..32692..27218..33199..51158..85874.144256..244623..428484..747152

..304...52160..96454..61508..63976..90312.144256.239368..392012..649748.1109780

..960..230048.279958.137320.124361.164300.244623.392012..635490.1018244.1657226

.2976.1000320.801574.303016.236858.299484.428484.649748.1018244.1614888.2549762

Links

R. H. Hardin, Table of n, a(n) for n = 1..363

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7

k=2: [order 8]

k=3: [order 14] for n>19

k=4: [order 24] for n>33

k=5: [order 24] for n>33

k=6: [order 32] for n>43

Example

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

Crossrefs

Column 1 is A280279.

Sequence in context: A055535 A072217 A229429 * A052686 A258781 A371207

Adjacent sequences: A281136 A281137 A281138 * A281140 A281141 A281142

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 15 2017

Status

approved