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%I #22 May 29 2017 21:19:06
%S 1,2,1,1,2,2,1,4,4,1,4,11,3,1,1,6,21,13,4,1,6,36,32,13,1,8,54,82,49,8,
%T 1,1,8,77,165,151,44,6,1,10,103,319,382,173,31,1,10,134,530,867,559,
%U 164,12,1,1,12,168,852,1789,1632,705,119,9
%N Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 6 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.
%H Andrew Howroyd, <a href="/A238551/b238551.txt">Table of n, a(n) for n = 3..971</a>
%H Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e The first 12 rows of T(n,k) are:
%e .\ k 0 1 2 3 4 5 6 7 8
%e n
%e 3 1 2 1
%e 4 1 2 2
%e 5 1 4 4
%e 6 1 4 11 3 1
%e 7 1 6 21 13 4
%e 8 1 6 36 32 13
%e 9 1 8 54 82 49 8 1
%e 10 1 8 77 165 151 44 6
%e 11 1 10 103 319 382 173 31
%e 12 1 10 134 530 867 559 164 12 1
%e 13 1 12 168 852 1789 1632 705 119 9
%e 14 1 12 207 1255 3409 4074 2406 618 66
%o (C++) See Gribble link.
%Y Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.
%K tabf,nonn
%O 3,2
%A _Christopher Hunt Gribble_, Feb 28 2014
%E Terms corrected and xrefs updated by _Christopher Hunt Gribble_, Apr 27 2015
%E Terms a(57) and beyond from _Andrew Howroyd_, May 29 2017
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