This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A236939 #20 Feb 17 2014 12:55:51 %S A236939 1,1,1,1,1,3,1,3,1,6,1,6,1,10,1,10,1,15,1,15,1,21,36,6,1,1,21,113,80, %T A236939 14,1,28,261,461,174,1,28,483,1665,1234,1,36,819,4725,6124,1,36,1266, %U A236939 11193,23259,1,45,1878,23646,73204 %N A236939 Number T(n,k) of equivalence classes of ways of placing k 10 X 10 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=10, 0<=k<=floor(n/10)^2, read by rows. %H A236939 Christopher Hunt Gribble, <a href="/A236939/a236939.cpp.txt">C++ program</a> %H A236939 Christopher Hunt Gribble, <a href="/A236939/a236939.txt">Example graphics</a> %F A236939 It appears that: %F A236939 T(n,0) = 1, n>= 10 %F A236939 T(n,1) = (floor((n-10)/2)+1)*(floor((n-10)/2+2))/2, n >= 10 %F A236939 T(c+2*10,2) = A131474(c+1)*(10-1) + A000217(c+1)*floor(10^2/4) + A014409(c+2), 0 <= c < 10, c even %F A236939 T(c+2*10,2) = A131474(c+1)*(10-1) + A000217(c+1)*floor((10-1)(10-3)/4) + A014409(c+2), 0 <= c < 10, c odd %F A236939 T(c+2*10,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((10-c-1)/2) + A131941(c+1)*floor((10-c)/2)) + S(c+1,3c+2,3), 0 <= c < 10 where %F A236939 S(c+1,3c+2,3) = %F A236939 A054252(2,3), c = 0 %F A236939 A236679(5,3), c = 1 %F A236939 A236560(8,3), c = 2 %F A236939 A236757(11,3), c = 3 %F A236939 A236800(14,3), c = 4 %F A236939 A236829(17,3), c = 5 %F A236939 A236865(20,3), c = 6 %F A236939 A236915(23,3), c = 7 %F A236939 A236936(26,3), c = 8 %F A236939 A236939(29,3), c = 9 %e A236939 The first 17 rows of T(n,k) are: %e A236939 .\ k 0 1 2 3 4 %e A236939 n %e A236939 10 1 1 %e A236939 11 1 1 %e A236939 12 1 3 %e A236939 13 1 3 %e A236939 14 1 6 %e A236939 15 1 6 %e A236939 16 1 10 %e A236939 17 1 10 %e A236939 18 1 15 %e A236939 19 1 15 %e A236939 20 1 21 36 6 1 %e A236939 21 1 21 113 80 14 %e A236939 22 1 28 261 461 174 %e A236939 23 1 28 483 1665 1234 %e A236939 24 1 36 819 4725 6124 %e A236939 25 1 36 1266 11193 23259 %e A236939 26 1 45 1878 23646 73204 %e A236939 . %e A236939 T(20,3) = 6 because the number of equivalence classes of ways of placing 3 10 X 10 square tiles in a 20 X 20 square under all symmetry operations of the square is 6. %Y A236939 Cf. A054252, A236679, A236560, A236757, A236800, A236829, A236865, A236915, A236936 %K A236939 tabf,nonn %O A236939 10,6 %A A236939 _Christopher Hunt Gribble_, Feb 01 2014