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A280961 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I A280961 #4 Jan 11 2017 15:17:43
%S A280961 1,2,2,4,9,4,11,42,42,11,30,205,241,205,30,82,997,1554,1554,997,82,
%T A280961 224,4850,9899,14106,9899,4850,224,612,23593,63085,126267,126267,
%U A280961 63085,23593,612,1672,114769,402077,1121528,1599234,1121528,402077,114769,1672,4568
%N A280961 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%C A280961 Table starts
%C A280961 ....1.......2.........4.........11...........30............82...........224
%C A280961 ....2.......9........42........205..........997..........4850.........23593
%C A280961 ....4......42.......241.......1554.........9899.........63085........402077
%C A280961 ...11.....205......1554......14106.......126267.......1121528.......9986376
%C A280961 ...30.....997......9899.....126267......1599234......20029500.....251270618
%C A280961 ...82....4850.....63085....1121528.....20029500.....346289502....6052621154
%C A280961 ..224...23593....402077....9986376....251270618....6052621154..148137367471
%C A280961 ..612..114769...2562733...88940022...3152475854..105777297118.3624578433814
%C A280961 .1672..558298..16334111..791997382..39530438497.1846875100200
%C A280961 .4568.2715861.104108376.7052519878.495721552160
%H A280961 R. H. Hardin, <a href="/A280961/b280961.txt">Table of n, a(n) for n = 1..112</a>
%F A280961 Empirical for column k:
%F A280961 k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
%F A280961 k=2: a(n) = 4*a(n-1) +4*a(n-2) +a(n-3) for n>4
%F A280961 k=3: [order 12] for n>16
%F A280961 k=4: [order 54] for n>57
%e A280961 Some solutions for n=4 k=4
%e A280961 ..0..1..2..0. .0..0..1..0. .0..0..1..2. .0..1..0..1. .0..1..0..0
%e A280961 ..2..0..1..2. .1..2..0..1. .2..1..0..1. .1..0..2..2. .1..2..1..2
%e A280961 ..0..1..0..1. .1..2..1..0. .2..0..1..2. .2..1..0..0. .2..1..2..1
%e A280961 ..2..0..2..2. .0..0..2..2. .1..2..0..0. .2..1..2..2. .0..0..1..0
%Y A280961 Column 1 is A021006(n-3).
%K A280961 nonn,tabl
%O A280961 1,2
%A A280961 _R. H. Hardin_, Jan 11 2017