A238558 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

1, 3, 4, 1, 3, 8, 1, 6, 18, 1, 6, 36, 32, 13, 1, 9, 64, 128, 87, 1, 9, 100, 308, 332, 1, 12, 146, 647, 1118, 451, 68, 1, 12, 200, 1160, 3022, 2756, 824, 1, 15, 264, 1958, 6882, 10076, 5009, 1, 15, 336, 3020, 13798, 28774, 24237, 4774, 346

Offset: 3

Author

Christopher Hunt Gribble, Feb 28 2014

Keywords

• tabf
• nonn

Examples

			The first 8 rows of T(n,k) are:
.\ k    0      1      2      3      4      5      6
n
3       1      3      4
4       1      3      8
5       1      6     18
6       1      6     36     32     13
7       1      9     64    128     87
8       1      9    100    308    332
9       1     12    146    647   1118    451     68
10      1     12    200   1160   3022   2756    824
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..971
• 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, A238559, A228168, A238581-A238583, A228169, A238586, A238592.

Extensions

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

Terms a(41) and beyond from Andrew Howroyd, May 29 2017