OFFSET
8,6
COMMENTS
The first 16 rows of T(n,k) are:
.\ k 0 1 2 3 4
n
8 1 1
9 1 1
10 1 3
11 1 3
12 1 6
13 1 6
14 1 10
15 1 10
16 1 15 25 5 1
17 1 15 79 65 14
18 1 21 187 377 174
19 1 21 351 1365 1234
20 1 28 606 3900 6124
21 1 28 948 9282 23259
22 1 36 1426 19726 73204
23 1 36 2026 38046 199436
LINKS
Christopher Hunt Gribble, Rows n = 8..23, flattened
Christopher Hunt Gribble, C++ program
FORMULA
It appears that:
T(n,0) = 1, n>= 8
T(n,1) = (floor((n-8)/2)+1)*(floor((n-8)/2+2))/2, n >= 8
T(c+2*8,2) = A131474(c+1)*(8-1) + A000217(c+1)*floor((8-1)(8-3)/4) + A014409(c+2), 0 <= c < 8, c odd
T(c+2*8,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((8-c-1)/2) + A131941(c+1)*floor((8-c)/2)) + S(c+1,3c+2,3), 0 <= c < 8 where
S(c+1,3c+2,3) =
A054252(2,3), c = 0
A236679(5,3), c = 1
A236560(8,3), c = 2
A236757(11,3), c = 3
A236800(14,3), c = 4
A236829(17,3), c = 5
A236865(20,3), c = 6
A236915(23,3), c = 7
EXAMPLE
T(16,3) = 5 because the number of equivalence classes of ways of placing 3 8 X 8 square tiles in an 16 X 16 square under all symmetry operations of the square is 5. The portrayal of an example from each equivalence class is:
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CROSSREFS
KEYWORD
tabf,nonn
AUTHOR
Christopher Hunt Gribble, Feb 01 2014
STATUS
approved