A257523 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows.

1, 2, 1, 2, 1, 4, 1, 4, 1, 6, 6, 1, 6, 14, 1, 8, 28, 1, 8, 44, 1, 10, 66, 20, 1, 10, 90, 64, 1, 12, 120, 168, 1, 12, 152, 320, 1, 14, 190, 572, 72, 1, 14, 230, 896, 328, 1, 16, 276, 1360, 984, 1, 16, 324, 1920, 2264, 1, 18, 378, 2660, 4528, 272

Offset

4,2

Links

Andrew Howroyd, Table of n, a(n) for n = 4..860

Christopher Hunt Gribble, C++ program

Example

The first 9 rows of T(n,k) are:
.\ k    0      1      2     3
n
4       1      2
5       1      2
6       1      4
7       1      4
8       1      6      6
9       1      6     14
10      1      8     28
11      1      8     44
12      1     10     66    20
13      1     10     90    64
14      1     12    120   168
15      1     12    152   320

Prog

(PARI)
T(n, k)={(4^k*binomial(n-3*k, k) + ((n%2==0||k%2==0)+(k%2==0)+(k==0)) * 4^((k+1)\2)*binomial((n-3*k-(k%2)-(n%2))/2, k\2))/4}
for(n=4, 15, for(k=0, (n\4), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

Crossrefs

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, 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: A072614 A287597 A238552 * A067044 A325677 A343411

Adjacent sequences: A257520 A257521 A257522 * A257524 A257525 A257526

Keyword

tabf,nonn

Author

Christopher Hunt Gribble, Apr 27 2015

Extensions

Terms a(24) and beyond by Andrew Howroyd, May 29 2017

Status

approved