A281837 - OEIS

%I #4 Jan 31 2017 11:17:47

%S 1,2,2,4,8,4,8,31,31,8,16,121,163,121,16,32,472,926,926,472,32,64,

%T 1841,5315,8240,5315,1841,64,128,7181,30387,74240,74240,30387,7181,

%U 128,256,28010,174121,663300,1053407,663300,174121,28010,256,512,109255,998069

%N 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.

%C Table starts

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

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

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

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

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

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

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

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

%C .256.109255..5720443..481128867..41858516870..3543794795757...304343654274741

%C .512.426157.32788987.4324987861.592613243866.78695552108964.10622958299884002

%H R. H. Hardin, <a href="/A281837/b281837.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

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

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

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

%e Some solutions for n=4 k=4

%e ..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..1..0..1. .0..0..0..1

%e ..0..0..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..1. .0..1..0..0

%e ..1..1..1..0. .0..1..0..1. .1..0..1..0. .1..1..0..1. .0..1..1..1

%e ..1..0..0..0. .1..1..0..1. .1..1..1..0. .0..0..0..0. .1..0..1..0

%Y Column 1 is A000079(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 31 2017