A281251 - OEIS

%I #4 Jan 18 2017 08:46:36

%S 0,0,0,0,0,0,1,12,12,1,2,139,443,139,2,9,1222,8489,8489,1222,9,34,

%T 9151,105368,197429,105368,9151,34,124,63138,1113148,3291920,3291920,

%U 1113148,63138,124,432,412070,10598099,47427679,76670685,47427679,10598099

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and 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...........1............2.............9............34

%C ....0........0.........12.........139.........1222..........9151.........63138

%C ....0.......12........443........8489.......105368.......1113148......10598099

%C ....1......139.......8489......197429......3291920......47427679.....622370435

%C ....2.....1222.....105368.....3291920.....76670685....1545796513...28420462973

%C ....9.....9151....1113148....47427679...1545796513...43504627489.1115818883427

%C ...34....63138...10598099...622370435..28420462973.1115818883427

%C ..124...412070...94350141..7668286112.491401215701

%C ..432..2585022..800540848.90290912746

%C .1464.15739317.6552843938

%H R. H. Hardin, <a href="/A281251/b281251.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>10

%F k=2: [order 10] for n>12

%F k=3: [order 35] for n>45

%e Some solutions for n=4 k=4

%e ..0..1..2..0. .0..0..1..0. .0..1..2..1. .0..1..0..1. .0..1..1..0

%e ..0..1..2..0. .2..0..1..2. .0..2..0..0. .0..2..0..1. .0..2..2..0

%e ..2..2..1..2. .1..2..2..1. .0..1..1..2. .1..2..2..2. .1..0..0..1

%e ..0..1..0..2. .1..0..0..2. .0..2..0..1. .0..1..0..1. .1..2..0..2

%Y Column 1 is A280309.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 18 2017