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 A236865 #15 Feb 17 2014 13:00:31 %S A236865 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, %T A236865 174,1,21,295,1225,1234,1,21,507,3465,6124,1,28,810,8358,23259,1,28, %U A236865 1214,17710,73204 %N 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. %C A236865 The first 13 rows of T(n,k) are: %C A236865 .\ k 0 1 2 3 4 5 6 7 8 9 %C A236865 n %C A236865 7 1 1 %C A236865 8 1 1 %C A236865 9 1 3 %C A236865 10 1 3 %C A236865 11 1 6 %C A236865 12 1 6 %C A236865 13 1 10 %C A236865 14 1 10 20 4 1 %C A236865 15 1 15 65 59 14 %C A236865 16 1 15 153 329 174 %C A236865 17 1 21 295 1225 1234 %C A236865 18 1 21 507 3465 6124 %C A236865 19 1 28 810 8358 23259 %C A236865 20 1 28 1214 17710 73204 %H A236865 Christopher Hunt Gribble, <a href="/A236865/a236865.cpp.txt">C++ program</a> %F A236865 It appears that: %F A236865 T(n,0) = 1, n>= 7 %F A236865 T(n,1) = (floor((n-7)/2)+1)*(floor((n-7)/2+2))/2, n >= 7 %F A236865 T(c+2*7,2) = A131474(c+1)*(7-1) + A000217(c+1)*floor(7^2/4) + A014409(c+2), 0 <= c < 7, c even %F A236865 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 %F A236865 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 %F A236865 S(c+1,3c+2,3) = %F A236865 A054252(2,3), c = 0 %F A236865 A236679(5,3), c = 1 %F A236865 A236560(8,3), c = 2 %F A236865 A236757(11,3), c = 3 %F A236865 A236800(14,3), c = 4 %F A236865 A236829(17,3), c = 5 %F A236865 A236865(20,3), c = 6 %e A236865 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: %e A236865 .___________________ ___________________ %e A236865 | | | | |_________| %e A236865 | | | | | | %e A236865 | | | | | | %e A236865 | . | . | | . | | %e A236865 | | | | | . | %e A236865 | | | | | | %e A236865 |_________|_________| |_________| | %e A236865 | | | | |_________| %e A236865 | | | | | | %e A236865 | | | | | | %e A236865 | . | | | . | | %e A236865 | | | | | | %e A236865 | | | | | | %e A236865 |_________|_________| |_________|_________| %e A236865 . %e A236865 .___________________ ___________________ %e A236865 | | | | | | %e A236865 | |_________| | | | %e A236865 | | | | |_________| %e A236865 | . | | | . | | %e A236865 | | | | | | %e A236865 | | . | | | | %e A236865 |_________| | |_________| . | %e A236865 | | | | | | %e A236865 | |_________| | | | %e A236865 | | | | |_________| %e A236865 | . | | | . | | %e A236865 | | | | | | %e A236865 | | | | | | %e A236865 |_________|_________| |_________|_________| %Y A236865 Cf. A054252, A236679, A236560, A236757, A236800, A236829, A236915, A236936, A236939. %K A236865 tabf,nonn %O A236865 7,6 %A A236865 _Christopher Hunt Gribble_, Jan 31 2014