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Number of nX2 0..3 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..3 order.
1

%I #7 Jun 06 2016 13:48:00

%S 2,10,105,1264,15418,188465,2304141,28171070,344428103,4211086174,

%T 51486063258,629484802987,7696279187803,94097130028610,

%U 1150461107685501,14065899352150196,171974109566120666,2102609553831755149

%N Number of nX2 0..3 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..3 order.

%C Column 2 of A273964.

%H R. H. Hardin, <a href="/A273961/b273961.txt">Table of n, a(n) for n = 1..46</a>

%F Empirical: a(n) = 14*a(n-1) -18*a(n-2) -54*a(n-3) +112*a(n-4) -30*a(n-5) -41*a(n-6) +18*a(n-7) for n>8

%F Empirical g.f.: 2*x -x^2*(10-35*x-26*x^2+152*x^3-85*x^4-49*x^5+30*x^6) / ( (x-1) *(x^2+x-1) *(18*x^4-41*x^3+6*x^2+12*x-1) ). - _R. J. Mathar_, Jun 06 2016

%e Some solutions for n=4

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

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

%e ..2..3. .2..0. .3..1. .1..3. .2..3. .1..2. .0..2. .1..0. .0..3. .1..2

%e ..0..2. .1..1. .2..3. .0..2. .0..2. .1..0. .0..1. .2..1. .3..0. .0..1

%Y Cf. A273964.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 05 2016