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%I #10 May 03 2018 07:02:28
%S 14,44,94,158,238,330,434,550,678,818,970,1134,1310,1498,1698,1910,
%T 2134,2370,2618,2878,3150,3434,3730,4038,4358,4690,5034,5390,5758,
%U 6138,6530,6934,7350,7778,8218,8670,9134,9610,10098,10598,11110,11634,12170,12718
%N Number of right triangles on an (n+1) X 3 grid.
%C Column 2 of A189814.
%H R. H. Hardin, <a href="/A189807/b189807.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 6*n^2 + 26*n - 42 for n>3.
%F Conjectures from _Colin Barker_, May 03 2018: (Start)
%F G.f.: 2*x*(7 + x + 2*x^2 - 3*x^3 + x^4 - 2*x^5) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F (End)
%e Some solutions for n=3:
%e ..3..0....0..1....2..1....1..1....2..0....3..0....1..1....2..2....0..0....3..1
%e ..0..0....0..0....1..0....0..1....2..1....2..0....0..2....1..1....0..2....1..1
%e ..3..1....3..1....3..0....1..2....3..0....3..2....2..2....3..1....3..0....3..2
%Y Cf. A189814.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 28 2011
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