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

2,2

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

Example

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

Prog

(C++) See Gribble link.

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.

Sequence in context: A220188 A238551 A289676 * A029256 A216501 A217463

Adjacent sequences: A238186 A238187 A238188 * A238190 A238191 A238192

Keyword

tabf,nonn

Author

Christopher Hunt Gribble, Feb 19 2014

Extensions

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

Status

approved