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A273968 T(n,k)=Number of nXk 0..3 arrays with no three equal values forming an isosceles triangle, and new values introduced in 0..3 order.

%I A273968 #4 Jun 05 2016 14:38:49
%S A273968 1,2,2,5,10,5,15,105,105,15,51,1264,1946,1264,51,187,13045,24587,
%T A273968 24587,13045,187,715,136063,211121,49534,211121,136063,715,2795,
%U A273968 1273961,2116450,36817,36817,2116450,1273961,2795,11051,11936399,15084593,40569
%N A273968 T(n,k)=Number of nXk 0..3 arrays with no three equal values forming an isosceles triangle, and new values introduced in 0..3 order.
%C A273968 Table starts
%C A273968 ......1..........2..........5....15.....51.....187......715......2795.....11051
%C A273968 ......2.........10........105..1264..13045..136063..1273961..11936399..95697853
%C A273968 ......5........105.......1946.24587.211121.2116450.15084593.112714143.511843593
%C A273968 .....15.......1264......24587.49534..36817...40569....36570.....90627.....89429
%C A273968 .....51......13045.....211121.36817....356......10........0.........0
%C A273968 ....187.....136063....2116450.40569.....10.......0........0
%C A273968 ....715....1273961...15084593.36570......0.......0
%C A273968 ...2795...11936399..112714143.90627......0
%C A273968 ..11051...95697853..511843593.89429
%C A273968 ..43947..800561388.2841058530
%C A273968 .175275.5824237329
%C A273968 .700075
%H A273968 R. H. Hardin, <a href="/A273968/b273968.txt">Table of n, a(n) for n = 1..82</a>
%F A273968 Empirical for column k:
%F A273968 k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
%e A273968 Some solutions for n=4 k=4
%e A273968 ..0..0..1..2. .0..1..2..1. .0..1..0..2. .0..0..1..0. .0..0..1..1
%e A273968 ..3..1..0..0. .0..3..2..3. .3..3..3..2. .2..3..3..3. .2..1..2..0
%e A273968 ..3..1..3..3. .0..3..2..3. .1..2..2..1. .3..2..1..1. .3..1..3..0
%e A273968 ..0..2..1..2. .2..1..0..0. .0..1..0..1. .1..0..2..2. .3..1..3..2
%Y A273968 Column 1 is A007581(n-1).
%K A273968 nonn,tabl
%O A273968 1,2
%A A273968 _R. H. Hardin_, Jun 05 2016