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

4,2

Links

Andrew Howroyd, Table of n, a(n) for n = 4..992

Christopher Hunt Gribble, C++ program

Example

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

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, A228168, A238581-A238583, A228169, A238586, A238592.

Sequence in context: A225224 A140216 A176514 * A077196 A023142 A225335

Adjacent sequences: A238556 A238557 A238558 * A238560 A238561 A238562

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

Status

approved