cp's OEIS Frontend

A236800 Number T(n,k) of equivalence classes of ways of placing k 5 X 5 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=5, 0<=k<=floor(n/5)^2, read by rows.

%I A236800 #21 Feb 18 2014 13:30:41
%S A236800 1,1,1,1,1,3,1,3,1,6,1,6,12,3,1,1,10,40,44,14,1,10,97,245,174,1,15,
%T A236800 193,925,1234,1,15,339,2640,6124,1,21,555,6617,27074,19336,4785,461,
%U A236800 23,1
%N A236800 Number T(n,k) of equivalence classes of ways of placing k 5 X 5 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=5, 0<=k<=floor(n/5)^2, read by rows.
%C A236800 The first 11 rows of T(n,k) are:
%C A236800 .\ k  0     1     2     3     4     5     6     7     8     9
%C A236800 n
%C A236800 5     1     1
%C A236800 6     1     1
%C A236800 7     1     3
%C A236800 8     1     3
%C A236800 9     1     6
%C A236800 10    1     6    12     3     1
%C A236800 11    1    10    40    44    14
%C A236800 12    1    10    97   245   174
%C A236800 13    1    15   193   925  1234
%C A236800 14    1    15   339  2640  6124
%C A236800 15    1    21   555  6617 27074 19336  4785   461    23     1
%H A236800 Christopher Hunt Gribble, <a href="/A236800/a236800.cpp.txt">C++ program</a>
%F A236800 It appears that:
%F A236800 T(n,0) = 1, n>= 5
%F A236800 T(n,1) = (floor((n-5)/2)+1)*(floor((n-5)/2+2))/2, n >= 5
%F A236800 T(c+2*5,2) = A131474(c+1)*(5-1) + A000217(c+1)*floor(5^2/4) + A014409(c+2), 0 <= c < 5, c even
%F A236800 T(c+2*5,2) = A131474(c+1)*(5-1) + A000217(c+1)*floor((5-1)(5-3)/4) + A014409(c+2), 0 <= c < 5, c odd
%F A236800 T(c+2*5,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((5-c-1)/2) + A131941(c+1)*floor((5-c)/2)) + S(c+1,3c+2,3), 0 <= c < 5 where
%F A236800 S(c+1,3c+2,3) =
%F A236800 A054252(2,3),  c = 0
%F A236800 A236679(5,3),  c = 1
%F A236800 A236560(8,3),  c = 2
%F A236800 A236757(11,3), c = 3
%F A236800 A236800(14,3), c = 4
%e A236800 T(10,3) = 3 because the number of equivalence classes of ways of placing 3 5 X 5 square tiles in an 10 X 10 square under all symmetry operations of the square is 3. The portrayal of an example from each equivalence class is:
%e A236800 ._______________      _______________      _______________
%e A236800 |       |       |    |       |_______|    |       |       |
%e A236800 |       |       |    |       |       |    |       |_______|
%e A236800 |   .   |   .   |    |   .   |       |    |   .   |       |
%e A236800 |       |       |    |       |   .   |    |       |       |
%e A236800 |_______|_______|    |_______|       |    |_______|   .   |
%e A236800 |       |       |    |       |_______|    |       |       |
%e A236800 |       |       |    |       |       |    |       |_______|
%e A236800 |   .   |       |    |   .   |       |    |   .   |       |
%e A236800 |       |       |    |       |       |    |       |       |
%e A236800 |_______|_______|    |_______|_______|    |_______|_______|
%Y A236800 Cf. A054252, A236679, A236560, A236757, A236829, A236865, A236915, A236936, A236939.
%K A236800 tabf,nonn
%O A236800 5,6
%A A236800 _Christopher Hunt Gribble_, Jan 31 2014