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 A236915 #30 Feb 17 2014 12:55:22 %S A236915 1,1,1,1,1,3,1,3,1,6,1,6,1,10,1,10,1,15,25,5,1,1,15,79,65,14,1,21,187, %T A236915 377,174,1,21,351,1365,1234,1,28,606,3900,6124,1,28,948,9282,23259,1, %U A236915 36,1426,19726,73204,1,36,2026,38046,199436 %N A236915 Number T(n,k) of equivalence classes of ways of placing k 8 X 8 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=8, 0<=k<=floor(n/8)^2, read by rows. %C A236915 The first 16 rows of T(n,k) are: %C A236915 .\ k 0 1 2 3 4 %C A236915 n %C A236915 8 1 1 %C A236915 9 1 1 %C A236915 10 1 3 %C A236915 11 1 3 %C A236915 12 1 6 %C A236915 13 1 6 %C A236915 14 1 10 %C A236915 15 1 10 %C A236915 16 1 15 25 5 1 %C A236915 17 1 15 79 65 14 %C A236915 18 1 21 187 377 174 %C A236915 19 1 21 351 1365 1234 %C A236915 20 1 28 606 3900 6124 %C A236915 21 1 28 948 9282 23259 %C A236915 22 1 36 1426 19726 73204 %C A236915 23 1 36 2026 38046 199436 %H A236915 Christopher Hunt Gribble, <a href="/A236915/b236915.txt">Rows n = 8..23, flattened</a> %H A236915 Christopher Hunt Gribble, <a href="/A236915/a236915.cpp.txt">C++ program</a> %F A236915 It appears that: %F A236915 T(n,0) = 1, n>= 8 %F A236915 T(n,1) = (floor((n-8)/2)+1)*(floor((n-8)/2+2))/2, n >= 8 %F A236915 T(c+2*8,2) = A131474(c+1)*(8-1) + A000217(c+1)*floor(8^2/4) + A014409(c+2), 0 <= c < 8, c even %F A236915 T(c+2*8,2) = A131474(c+1)*(8-1) + A000217(c+1)*floor((8-1)(8-3)/4) + A014409(c+2), 0 <= c < 8, c odd %F A236915 T(c+2*8,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((8-c-1)/2) + A131941(c+1)*floor((8-c)/2)) + S(c+1,3c+2,3), 0 <= c < 8 where %F A236915 S(c+1,3c+2,3) = %F A236915 A054252(2,3), c = 0 %F A236915 A236679(5,3), c = 1 %F A236915 A236560(8,3), c = 2 %F A236915 A236757(11,3), c = 3 %F A236915 A236800(14,3), c = 4 %F A236915 A236829(17,3), c = 5 %F A236915 A236865(20,3), c = 6 %F A236915 A236915(23,3), c = 7 %e A236915 T(16,3) = 5 because the number of equivalence classes of ways of placing 3 8 X 8 square tiles in an 16 X 16 square under all symmetry operations of the square is 5. The portrayal of an example from each equivalence class is: %e A236915 ._____________________ _____________________ %e A236915 | | | | |__________| %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 | . | . | | . | | %e A236915 | | | | | . | %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 |__________|__________| |__________| | %e A236915 | | | | |__________| %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 | . | | | . | | %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 |__________|__________| |__________|__________| %e A236915 . %e A236915 ._____________________ _____________________ %e A236915 | | | | | | %e A236915 | |__________| | | | %e A236915 | | | | |__________| %e A236915 | . | | | . | | %e A236915 | | | | | | %e A236915 | | . | | | | %e A236915 | | | | | . | %e A236915 |__________| | |__________| | %e A236915 | | | | | | %e A236915 | |__________| | | | %e A236915 | | | | |__________| %e A236915 | . | | | . | | %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 | | | | | | %e A236915 |__________|__________| |__________|__________| %e A236915 . %e A236915 ._____________________ %e A236915 | | | %e A236915 | | | %e A236915 | | | %e A236915 | . |__________| %e A236915 | | | %e A236915 | | | %e A236915 | | | %e A236915 |__________| . | %e A236915 | | | %e A236915 | | | %e A236915 | | | %e A236915 | . |__________| %e A236915 | | | %e A236915 | | | %e A236915 | | | %e A236915 |__________|__________| %Y A236915 Cf. A054252, A236679, A236560, A236757, A236800, A236829, A236865, A236936, A236939. %K A236915 tabf,nonn %O A236915 8,6 %A A236915 _Christopher Hunt Gribble_, Feb 01 2014