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A238592 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=3*floor(n/3), read by rows.

%I A238592 #18 May 29 2017 21:11:17
%S A238592 1,4,9,2,1,4,18,8,1,8,42,28,1,8,77,165,151,44,6,1,12,133,521,891,543,
%T A238592 106,1,12,200,1160,3022,2756,824,1,16,288,2260,8443,13336,9364,2819,
%U A238592 387,20,1,16,387,3867,19833,48418,58731,34797,9462,900
%N A238592 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=3*floor(n/3), read by rows.
%H A238592 Andrew Howroyd, <a href="/A238592/b238592.txt">Table of n, a(n) for n = 3..989</a>
%H A238592 Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e A238592 The first 6 rows of T(n,k) are:
%e A238592 .\ k    0      1      2      3      4      5      6
%e A238592 n
%e A238592 3       1      4      9      2
%e A238592 4       1      4     18      8
%e A238592 5       1      8     42     28
%e A238592 6       1      8     77    165    151     44      6
%e A238592 7       1     12    133    521    891    543    106
%e A238592 8       1     12    200   1160   3022   2756    824
%o A238592 (C++) See Gribble link.
%Y A238592 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.
%K A238592 tabf,nonn
%O A238592 3,2
%A A238592 _Christopher Hunt Gribble_, Mar 01 2014
%E A238592 Terms corrected and xrefs updated by _Christopher Hunt Gribble_, Apr 27 2015
%E A238592 Terms a(36) and beyond from _Andrew Howroyd_, May 29 2017