A236865 Number T(n,k) of equivalence classes of ways of placing k 7 X 7 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=7, 0<=k<=floor(n/7)^2, read by rows.
1, 1, 1, 1, 1, 3, 1, 3, 1, 6, 1, 6, 1, 10, 1, 10, 20, 4, 1, 1, 15, 65, 59, 14, 1, 15, 153, 329, 174, 1, 21, 295, 1225, 1234, 1, 21, 507, 3465, 6124, 1, 28, 810, 8358, 23259, 1, 28, 1214, 17710, 73204
Offset: 7
Examples
T(14,3) = 4 because the number of equivalent classes of ways of placing 3 7 X 7 square tiles in an 14 X 14 square under all symmetry operations of the square is 4. The portrayal of an example from each equivalence class is: .___________________ ___________________ | | | | |_________| | | | | | | | | | | | | | . | . | | . | | | | | | | . | | | | | | | |_________|_________| |_________| | | | | | |_________| | | | | | | | | | | | | | . | | | . | | | | | | | | | | | | | | |_________|_________| |_________|_________| . .___________________ ___________________ | | | | | | | |_________| | | | | | | | |_________| | . | | | . | | | | | | | | | | . | | | | |_________| | |_________| . | | | | | | | | |_________| | | | | | | | |_________| | . | | | . | | | | | | | | | | | | | | |_________|_________| |_________|_________|
Links
- Christopher Hunt Gribble, C++ program
Formula
It appears that:
T(n,0) = 1, n>= 7
T(n,1) = (floor((n-7)/2)+1)*(floor((n-7)/2+2))/2, n >= 7
T(c+2*7,2) = A131474(c+1)*(7-1) + A000217(c+1)*floor((7-1)(7-3)/4) + A014409(c+2), 0 <= c < 7, c odd
T(c+2*7,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((7-c-1)/2) + A131941(c+1)*floor((7-c)/2)) + S(c+1,3c+2,3), 0 <= c < 7 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
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