A238189 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 4 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.

1, 2, 1, 1, 2, 2, 1, 4, 7, 3, 1, 1, 4, 13, 10, 4, 1, 6, 23, 33, 22, 6, 1, 1, 6, 34, 68, 72, 30, 6, 1, 8, 49, 139, 204, 145, 54, 8, 1, 1, 8, 65, 230, 467, 476, 269, 70, 9, 1, 10, 85, 377, 961, 1348, 1080, 472, 111, 12, 1, 1, 10, 106, 552, 1767, 3188, 3454, 2156

Offset: 2

Author

Christopher Hunt Gribble, Feb 19 2014

Keywords

• tabf
• nonn

Examples

			The first 10 rows of T(n,k) are:
  k  0     1     2     3     4     5     6     7     8     9    10
n
2    1     2     1
3    1     2     2
4    1     4     7     3     1
5    1     4    13    10     4
6    1     6    23    33    22     6     1
7    1     6    34    68    72    30     6
8    1     8    49   139   204   145    54     8     1
9    1     8    65   230   467   476   269    70     9
10   1    10    85   377   961  1348  1080   472   111    12     1
11   1    10   106   552  1767  3188  3454  2156   779   140    12
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..967 (terms n=2..127 from Christopher Hunt Gribble)
• Christopher Hunt Gribble, C++ program

Crossrefs

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Apr 25 2015