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Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.
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%I #33 May 29 2017 21:28:59

%S 1,2,2,1,2,4,1,4,13,10,4,1,4,23,35,23,1,6,40,101,125,54,10,1,6,58,206,

%T 403,336,106,1,8,83,392,1056,1438,956,240,25,1,8,109,641,2281,4424,

%U 4718,2409,473,1,10,142,1011,4429,11370,17252,14478,6094,1020,70

%N Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.

%H Andrew Howroyd, <a href="/A231145/b231145.txt">Table of n, a(n) for n = 2..967</a> (terms n=2..71 from Christopher Hunt Gribble)

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

%e The first 8 rows of T(n,k) are:

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

%e n

%e 2 1 2 2

%e 3 1 2 4

%e 4 1 4 13 10 4

%e 5 1 4 23 35 23

%e 6 1 6 40 101 125 54 10

%e 7 1 6 58 206 403 336 106

%e 8 1 8 83 392 1056 1438 956 240 25

%e 9 1 8 109 641 2281 4424 4718 2409 473

%o (C++) See Gribble link.

%Y Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

%K tabf,nonn

%O 2,2

%A _Christopher Hunt Gribble_, Feb 23 2014

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