%I #23 May 29 2017 21:10:50

%S 1,5,16,19,9,1,1,5,32,73,66,10,1,10,85,377,961,1348,1080,472,111,12,1,

%T 1,10,142,1011,4429,11370,17252,14478,6094,1020,70,1,15,236,2280,

%U 14203,56571,146212,244063,261847,179063,77974,21422,3637,368,24,1

%N Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=5*floor(n/2), read by rows.

%H Andrew Howroyd, <a href="/A238586/b238586.txt">Table of n, a(n) for n = 2..937</a>

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

%e The first 4 rows of T(n,k) are:

%e .\k 0 1 2 3 4 5 6 7 8 9 10

%e n

%e 2 1 5 16 19 9 1

%e 3 1 5 32 73 66 10

%e 4 1 10 85 377 961 1348 1080 472 111 12 1

%e 5 1 10 142 1011 4429 11370 17252 14478 6094 1020 70

%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-A238559, A228168, A238581-A238583, A228169, A238592.

%K tabf,nonn

%O 2,2

%A _Christopher Hunt Gribble_, Mar 01 2014

%E Terms corrected and crossrefs updated by _Christopher Hunt Gribble_, Apr 27 2015

%E Terms a(36) and beyond from _Andrew Howroyd_, May 29 2017