A317465 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 16, 18, 0, 0, 61, 107, 107, 61, 0, 0, 209, 636, 1429, 636, 209, 0, 0, 702, 3893, 16809, 16809, 3893, 702, 0, 0, 2381, 23769, 203786, 386855, 203786, 23769, 2381, 0, 0, 8069, 145280, 2461839, 9178195, 9178195, 2461839

Offset

1,5

Comments

Table starts

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

.0....3......5........18...........61............209...............702

.0....5.....16.......107..........636...........3893.............23769

.0...18....107......1429........16809.........203786...........2461839

.0...61....636.....16809.......386855........9178195.........217053933

.0..209...3893....203786......9178195......426934467.......19791556259

.0..702..23769...2461839....217053933....19791556259.....1798167135483

.0.2381.145280..29797355...5142922330...919311610591...163704740864606

.0.8069.887980.360606527.121842389647.42696124087673.14901625879985868

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 12] for n>14

k=4: [order 28] for n>29

k=5: [order 61] for n>64

Example

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

Crossrefs

Column 2 is A303684.

Sequence in context: A316686 A304767 A316511 * A051174 A273089 A362021

Adjacent sequences: A317462 A317463 A317464 * A317466 A317467 A317468

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 28 2018

Status

approved