A238551 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 6 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, 2, 1, 1, 2, 2, 1, 4, 4, 1, 4, 11, 3, 1, 1, 6, 21, 13, 4, 1, 6, 36, 32, 13, 1, 8, 54, 82, 49, 8, 1, 1, 8, 77, 165, 151, 44, 6, 1, 10, 103, 319, 382, 173, 31, 1, 10, 134, 530, 867, 559, 164, 12, 1, 1, 12, 168, 852, 1789, 1632, 705, 119, 9

Offset

3,2

Links

Andrew Howroyd, Table of n, a(n) for n = 3..971

Christopher Hunt Gribble, C++ program

Example

The first 12 rows of T(n,k) are:
.\ k  0     1     2     3     4     5     6     7     8
n
3     1     2     1
4     1     2     2
5     1     4     4
6     1     4    11     3     1
7     1     6    21    13     4
8     1     6    36    32    13
9     1     8    54    82    49     8     1
10    1     8    77   165   151    44     6
11    1    10   103   319   382   173    31
12    1    10   134   530   867   559   164    12     1
13    1    12   168   852  1789  1632   705   119     9
14    1    12   207  1255  3409  4074  2406   618    66

Prog

(C++) See Gribble link.

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, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

Sequence in context: A024165 A023191 A220188 * A289676 A238189 A029256

Adjacent sequences: A238548 A238549 A238550 * A238552 A238553 A238554

Keyword

tabf,nonn

Author

Christopher Hunt Gribble, Feb 28 2014

Extensions

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

Terms a(57) and beyond from Andrew Howroyd, May 29 2017

Status

approved