|
%I #4 Jan 24 2017 08:36:19
%S 0,0,0,0,0,0,0,5,1,0,0,18,68,6,0,0,141,621,815,57,0,0,602,2426,3374,
%T 4172,310,0,0,2180,6955,12133,15508,18020,1508,0,0,7006,16656,31300,
%U 50510,53568,62882,6854,0,0,20979,36578,67834,119319,154722,162919,201551
%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C .0......0.......0.......0.......0........0........0........0........0.........0
%C .0......0.......5......18.....141......602.....2180.....7006....20979.....59698
%C .0......1......68.....621....2426.....6955....16656....36578....76332....153813
%C .0......6.....815....3374...12133....31300....67834...136056...264286....498750
%C .0.....57....4172...15508...50510...119319...243040...458646...836348...1499031
%C .0....310...18020...53568..154722...347316...692421..1275888..2241388...3864672
%C .0...1508...62882..162919..430995...919632..1818257..3326246..5744641...9601436
%C .0...6854..201551..463916.1166392..2383814..4578736..8300608.14212419..23352928
%C .0..29487..605398.1262057.3018274..5976640.11105124.19678234.33449458..54649755
%C .0.122326.1743548.3344312.7606230.14598286.26461889.45643798.76274137.124061416
%H R. H. Hardin, <a href="/A281563/b281563.txt">Table of n, a(n) for n = 1..242</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: [order 12]
%F k=3: [order 21] for n>29
%F k=4: [order 24] for n>34
%F k=5: [order 29] for n>46
%F k=6: [order 32] for n>52
%F k=7: [order 35] for n>58
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: [order 14] for n>15
%F n=3: [order 12] for n>20
%F n=4: [order 15] for n>24
%F n=5: [order 18] for n>28
%F n=6: [order 21] for n>37
%F n=7: [order 24] for n>46
%e Some solutions for n=4 k=4
%e ..0..1..0..0. .0..0..1..0. .0..1..0..1. .0..0..1..1. .0..1..1..0
%e ..0..1..0..1. .0..1..1..0. .1..0..1..0. .0..1..1..0. .1..0..1..0
%e ..1..0..1..1. .1..0..0..0. .1..0..1..1. .0..0..0..1. .1..1..1..0
%e ..1..0..0..1. .1..0..1..0. .1..0..0..0. .0..1..0..1. .1..0..1..0
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 24 2017
| 