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 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. 9
 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, 193, 925, 1234, 1, 15, 339, 2640, 6124, 1, 21, 555, 6617, 27074, 19336, 4785, 461, 23, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,6 COMMENTS The first 11 rows of T(n,k) are: .\ k 0 1 2 3 4 5 6 7 8 9 n 5 1 1 6 1 1 7 1 3 8 1 3 9 1 6 10 1 6 12 3 1 11 1 10 40 44 14 12 1 10 97 245 174 13 1 15 193 925 1234 14 1 15 339 2640 6124 15 1 21 555 6617 27074 19336 4785 461 23 1 LINKS Table of n, a(n) for n=5..49. Christopher Hunt Gribble, C++ program FORMULA It appears that: T(n,0) = 1, n>= 5 T(n,1) = (floor((n-5)/2)+1)*(floor((n-5)/2+2))/2, n >= 5 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 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 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 S(c+1,3c+2,3) = A054252(2,3), c = 0 A236679(5,3), c = 1 A236560(8,3), c = 2 A236757(11,3), c = 3 A236800(14,3), c = 4 EXAMPLE 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: ._______________ _______________ _______________ | | | | |_______| | | | | | | | | | | |_______| | . | . | | . | | | . | | | | | | | . | | | | |_______|_______| |_______| | |_______| . | | | | | |_______| | | | | | | | | | | |_______| | . | | | . | | | . | | | | | | | | | | | |_______|_______| |_______|_______| |_______|_______| CROSSREFS Cf. A054252, A236679, A236560, A236757, A236829, A236865, A236915, A236936, A236939. Sequence in context: A236915 A236865 A236829 * A367628 A126212 A357858 Adjacent sequences: A236797 A236798 A236799 * A236801 A236802 A236803 KEYWORD tabf,nonn AUTHOR Christopher Hunt Gribble, Jan 31 2014 STATUS approved

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Last modified December 5 23:11 EST 2023. Contains 367594 sequences. (Running on oeis4.)