%I #24 May 29 2017 21:27:44

%S 1,3,4,1,1,3,8,3,1,6,23,33,22,6,1,1,6,40,101,125,54,10,1,9,68,262,534,

%T 532,276,74,12,1,1,9,98,509,1551,2505,2196,971,219,20,1,12,139,927,

%U 3731,8772,12069,9506,4366,1160,179,16,1,1,12,182,1479,7644,24024

%N Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 6 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=3*floor(n/2), read by rows.

%H Andrew Howroyd, <a href="/A238550/b238550.txt">Table of n, a(n) for n = 2..953</a> (terms n=2..69 from Christopher Hunt Gribble)

%H Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>

%e The first 6 rows of T(n,k) are:

%e .\ k 0 1 2 3 4 5 6 7 8 9

%e n

%e 2 1 3 4 1

%e 3 1 3 8 3

%e 4 1 6 23 33 22 6 1

%e 5 1 6 40 101 125 54 10

%e 6 1 9 68 262 534 532 276 74 12 1

%e 7 1 9 98 509 1551 2505 2196 971 219 20

%o (C++) See Gribble link.

%Y Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238551, A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586, A238592.

%K tabf,nonn

%O 2,2

%A _Christopher Hunt Gribble_, Feb 28 2014

%E Terms corrected and xrefs updated by _Christopher Hunt Gribble_, Apr 26 2015