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T(n,k) = Number of n X k 0..1 arrays with exactly n+k-1 having value 1 and no three 1's forming an isosceles right triangle.
7

%I #6 Jun 22 2022 11:23:55

%S 1,1,1,1,0,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,9,0,9,0,1,1,1,6,8,8,6,

%T 1,1,1,0,16,8,12,8,16,0,1,1,1,66,71,58,58,71,66,1,1,1,0,95,212,367,

%U 192,367,212,95,0,1,1,1,177,731,1952,838,838,1952,731,177,1,1,1,0,493,1840,10854

%N T(n,k) = Number of n X k 0..1 arrays with exactly n+k-1 having value 1 and no three 1's forming an isosceles right triangle.

%C Table starts

%C .1.1..1...1.....1.....1......1......1......1......1.......1......1.....1....1.1

%C .1.0..1...0.....1.....0......1......0......1......0.......1......0.....1....0.1

%C .1.1..0...1.....9.....6.....16.....66.....95....177.....493...1153..2238.5011

%C .1.0..1...0.....8.....8.....71....212....731...1840....5953..18632.54705

%C .1.1..9...8....12....58....367...1952..10854..28952..111036.509073

%C .1.0..6...8....58...192....838...4968..37436.250516.1268025

%C .1.1.16..71...367...838...4892..26051.198970

%C .1.0.66.212..1952..4968..26051.230268

%C .1.1.95.731.10854.37436.198970

%H R. H. Hardin, <a href="/A272965/b272965.txt">Table of n, a(n) for n = 1..126</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1);

%F k=2: a(n) = a(n-2);

%F k=3: a(n) = [linear recurrence of order 32].

%e Some solutions for n=6, k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,24

%A _R. H. Hardin_, May 11 2016