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A238558 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

%I A238558 #18 May 29 2017 21:11:51
%S A238558 1,3,4,1,3,8,1,6,18,1,6,36,32,13,1,9,64,128,87,1,9,100,308,332,1,12,
%T A238558 146,647,1118,451,68,1,12,200,1160,3022,2756,824,1,15,264,1958,6882,
%U A238558 10076,5009,1,15,336,3020,13798,28774,24237,4774,346
%N A238558 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 8 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 A238558 Andrew Howroyd, <a href="/A238558/b238558.txt">Table of n, a(n) for n = 3..971</a>
%H A238558 Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e A238558 The first 8 rows of T(n,k) are:
%e A238558 .\ k    0      1      2      3      4      5      6
%e A238558 n
%e A238558 3       1      3      4
%e A238558 4       1      3      8
%e A238558 5       1      6     18
%e A238558 6       1      6     36     32     13
%e A238558 7       1      9     64    128     87
%e A238558 8       1      9    100    308    332
%e A238558 9       1     12    146    647   1118    451     68
%e A238558 10      1     12    200   1160   3022   2756    824
%o A238558 (C++)  See Gribble link.
%Y A238558 Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557, A238559, A228168, A238581-A238583, A228169, A238586, A238592.
%K A238558 tabf,nonn
%O A238558 3,2
%A A238558 _Christopher Hunt Gribble_, Feb 28 2014
%E A238558 Terms corrected and xrefs updated by _Christopher Hunt Gribble_, Apr 27 2015
%E A238558 Terms a(41) and beyond from _Andrew Howroyd_, May 29 2017