A238559 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.

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, 90, 31, 1, 15, 121, 193, 98, 13, 1, 1, 15, 162, 360, 275, 66, 6, 1, 18, 212, 664, 672, 250, 31, 1, 18, 266, 1080, 1408, 672, 110, 1, 21, 329, 1711, 2797, 1772, 432, 23, 1

Offset: 4

Author

Christopher Hunt Gribble, Feb 28 2014

Keywords

• tabf
• nonn

Examples

			The first 11 rows of T(n,k) are:
.\  k   0      1      2      3      4     5     6
n
4       1      3      1
5       1      3      2
6       1      6      4
7       1      6      6
8       1      9     17      5      1
9       1      9     32     18      4
10      1     12     56     46     13
11      1     12     84     90     31
12      1     15    121    193     98    13     1
13      1     15    162    360    275    66     6
14      1     18    212    664    672   250    31
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 4..992
• Christopher Hunt Gribble, C++ program

Crossrefs

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.

Extensions

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(31) and beyond from Andrew Howroyd, May 29 2017