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T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no three 1s forming an isosceles right triangle.
8

%I #4 May 11 2016 14:54:42

%S 1,2,2,3,6,3,4,10,10,4,5,21,24,21,5,6,34,24,24,34,6,7,62,107,60,107,

%T 62,7,8,100,236,210,210,236,100,8,9,171,499,637,768,637,499,171,9,10,

%U 276,1228,1840,1898,1898,1840,1228,276,10,11,458,2753,5792,8211,7468,8211,5792

%N T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no three 1s forming an isosceles right triangle.

%C Table starts

%C .1...2....3.....4......5......6.......7.......8.......9......10.......11

%C .2...6...10....21.....34.....62.....100.....171.....276.....458......740

%C .3..10...24....24....107....236.....499....1228....2753....6292....14751

%C .4..21...24....60....210....637....1840....5792...18556...54034...160246

%C .5..34..107...210....768...1898....8211...37402..192579..635086..2366644

%C .6..62..236...637...1898...7468...26052..138476..831738.4677062.23090612

%C .7.100..499..1840...8211..26052..131056..648178.4336294

%C .8.171.1228..5792..37402.138476..648178.4614732

%C .9.276.2753.18556.192579.831738.4336294

%H R. H. Hardin, <a href="/A272958/b272958.txt">Table of n, a(n) for n = 1..126</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) -a(n-2)

%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-3) -3*a(n-4) +a(n-5) +a(n-6)

%F k=3: [order 72]

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 11 2016