A281837 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 163, 121, 16, 32, 472, 926, 926, 472, 32, 64, 1841, 5315, 8240, 5315, 1841, 64, 128, 7181, 30387, 74240, 74240, 30387, 7181, 128, 256, 28010, 174121, 663300, 1053407, 663300, 174121, 28010, 256, 512, 109255, 998069

Offset

1,2

Comments

Table starts

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

...2......8.......31........121..........472...........1841..............7181

...4.....31......163........926.........5315..........30387............174121

...8....121......926.......8240........74240.........663300...........5954670

..16....472.....5315......74240......1053407.......14783996.........208837689

..32...1841....30387.....663300.....14783996......324602161........7184856176

..64...7181...174121....5954670....208837689.....7184856176......249711414322

.128..28010...998069...53530609...2957076233...159608206156.....8720904906157

.256.109255..5720443..481128867..41858516870..3543794795757...304343654274741

.512.426157.32788987.4324987861.592613243866.78695552108964.10622958299884002

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

k=3: [order 7] for n>8

k=4: [order 23] for n>24

k=5: [order 97] for n>99

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A317004 A316822 A317572 * A299081 A299844 A299001

Adjacent sequences: A281834 A281835 A281836 * A281838 A281839 A281840

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 31 2017

Status

approved