

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
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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



FORMULA

It appears that:
T(n,0) = 1, n>= 5
T(n,1) = (floor((n5)/2)+1)*(floor((n5)/2+2))/2, n >= 5
T(c+2*5,3) = (c+1)(c+2)/2(2*A002623(c1)*floor((5c1)/2) + A131941(c+1)*floor((5c)/2)) + S(c+1,3c+2,3), 0 <= c < 5 where
S(c+1,3c+2,3) =


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



KEYWORD

tabf,nonn


AUTHOR



STATUS

approved



