A317036 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 30, 28, 16, 32, 94, 82, 82, 94, 32, 64, 284, 280, 354, 280, 284, 64, 128, 752, 842, 1718, 1718, 842, 752, 128, 256, 2244, 2591, 7523, 11368, 7523, 2591, 2244, 256, 512, 6532, 8141, 33798, 66728, 66728, 33798, 8141, 6532, 512

Offset

1,2

Comments

Table starts

...1....2.....4......8.......16........32..........64..........128

...2....4....14.....28.......94.......284.........752.........2244

...4...14....30.....82......280.......842........2591.........8141

...8...28....82....354.....1718......7523.......33798.......153703

..16...94...280...1718....11368.....66728......417156......2714271

..32..284...842...7523....66728....559097.....4939166.....46085330

..64..752..2591..33798...417156...4939166....64983838....900623946

.128.2244..8141.153703..2714271..46085330...900623946..19235095363

.256.6532.25387.700615.17610616.435634601.12923660734.426907974013

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 65] for n>67

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A304347 A316218 A305642 * A305911 A317153 A316883

Adjacent sequences: A317033 A317034 A317035 * A317037 A317038 A317039

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 19 2018

Status

approved