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%I #20 May 29 2017 21:12:47
%S 1,3,1,1,3,2,1,6,4,1,6,6,1,9,17,5,1,1,9,32,18,4,1,12,56,46,13,1,12,84,
%T 90,31,1,15,121,193,98,13,1,1,15,162,360,275,66,6,1,18,212,664,672,
%U 250,31,1,18,266,1080,1408,672,110,1,21,329,1711,2797,1772,432,23,1
%N Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.
%H Andrew Howroyd, <a href="/A238559/b238559.txt">Table of n, a(n) for n = 4..992</a>
%H Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e The first 11 rows of T(n,k) are:
%e .\ k 0 1 2 3 4 5 6
%e n
%e 4 1 3 1
%e 5 1 3 2
%e 6 1 6 4
%e 7 1 6 6
%e 8 1 9 17 5 1
%e 9 1 9 32 18 4
%e 10 1 12 56 46 13
%e 11 1 12 84 90 31
%e 12 1 15 121 193 98 13 1
%e 13 1 15 162 360 275 66 6
%e 14 1 18 212 664 672 250 31
%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, A228168, A238581-A238583, A228169, A238586, A238592.
%K tabf,nonn
%O 4,2
%A _Christopher Hunt Gribble_, Feb 28 2014
%E Terms corrected and xrefs updated by _Christopher Hunt Gribble_, Apr 27 2015
%E Terms a(31) and beyond from _Andrew Howroyd_, May 29 2017
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