cp's OEIS Frontend

A236936 Number T(n,k) of equivalence classes of ways of placing k 9 X 9 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=9, 0<=k<=floor(n/9)^2, read by rows.

%I A236936 #21 Feb 17 2014 12:59:17
%S A236936 1,1,1,1,1,3,1,3,1,6,1,6,1,10,1,10,1,15,1,15,30,5,1,1,21,96,74,14,1,
%T A236936 21,221,413,174,1,28,417,1525,1234,1,28,705,4290,6124,1,36,1107,10269,
%U A236936 23259,1,36,1638,21630,73204,1,45,2334,41790,199436
%N A236936 Number T(n,k) of equivalence classes of ways of placing k 9 X 9 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=9, 0<=k<=floor(n/9)^2, read by rows.
%H A236936 Christopher Hunt Gribble, <a href="/A236936/a236936.cpp.txt">C++ program</a>
%H A236936 Christopher Hunt Gribble, <a href="/A236936/a236936.txt">Example graphics</a>
%F A236936 It appears that:
%F A236936 T(n,0) = 1, n>= 9
%F A236936 T(n,1) = (floor((n-9)/2)+1)*(floor((n-9)/2+2))/2, n >= 9
%F A236936 T(c+2*9,2) =  A131474(c+1)*(9-1) + A000217(c+1)*floor(9^2/4) + A014409(c+2), 0 <= c < 9, c even
%F A236936 T(c+2*9,2) = A131474(c+1)*(9-1) + A000217(c+1)*floor((9-1)(9-3)/4) + A014409(c+2), 0 <= c < 9, c odd
%F A236936 T(c+2*9,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((9-c-1)/2) + A131941(c+1)*floor((9-c)/2)) + S(c+1,3c+2,3), 0 <= c < 9 where
%F A236936 S(c+1,3c+2,3) =
%F A236936 A054252(2,3),  c = 0
%F A236936 A236679(5,3),  c = 1
%F A236936 A236560(8,3),  c = 2
%F A236936 A236757(11,3), c = 3
%F A236936 A236800(14,3), c = 4
%F A236936 A236829(17,3), c = 5
%F A236936 A236865(20,3), c = 6
%F A236936 A236915(23,3), c = 7
%F A236936 A236936(26,3), c = 8
%e A236936 The first 17 rows of T(n,k) are:
%e A236936 .\ k  0      1      2      3      4
%e A236936 n
%e A236936 9     1      1
%e A236936 10    1      1
%e A236936 11    1      3
%e A236936 12    1      3
%e A236936 13    1      6
%e A236936 14    1      6
%e A236936 15    1     10
%e A236936 16    1     10
%e A236936 17    1     15
%e A236936 18    1     15     30      5      1
%e A236936 19    1     21     96     74     14
%e A236936 20    1     21    221    413    174
%e A236936 21    1     28    417   1525   1234
%e A236936 22    1     28    705   4290   6124
%e A236936 23    1     36   1107  10269  23259
%e A236936 24    1     36   1638  21630  73204
%e A236936 25    1     45   2334  41790 199436
%e A236936 .
%e A236936 T(18,3) = 5 because the number of equivalence classes of ways of placing 3 9 X 9 square tiles in an 18 X 18 square under all symmetry operations of the square is 5.
%Y A236936 Cf. A054252, A236679, A236560, A236757, A236800, A236829, A236865, A236915, A236939.
%K A236936 tabf,nonn
%O A236936 9,6
%A A236936 _Christopher Hunt Gribble_, Feb 01 2014