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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. 9
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, 14, 1, 28, 261, 461, 174, 1, 28, 483, 1665, 1234, 1, 36, 819, 4725, 6124, 1, 36, 1266, 11193, 23259, 1, 45, 1878, 23646, 73204 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,6

LINKS

Table of n, a(n) for n=10..64.

Christopher Hunt Gribble, C++ program

Christopher Hunt Gribble, Example graphics

FORMULA

It appears that:

T(n,0) = 1, n>= 10

T(n,1) = (floor((n-10)/2)+1)*(floor((n-10)/2+2))/2, n >= 10

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

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

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

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

A236829(17,3), c = 5

A236865(20,3), c = 6

A236915(23,3), c = 7

A236936(26,3), c = 8

A236939(29,3), c = 9

EXAMPLE

The first 17 rows of T(n,k) are:

.\ k  0     1     2     3     4

n

10    1     1

11    1     1

12    1     3

13    1     3

14    1     6

15    1     6

16    1    10

17    1    10

18    1    15

19    1    15

20    1    21    36     6     1

21    1    21   113    80    14

22    1    28   261   461   174

23    1    28   483  1665  1234

24    1    36   819  4725  6124

25    1    36  1266 11193 23259

26    1    45  1878 23646 73204

.

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.

CROSSREFS

Cf. A054252, A236679, A236560, A236757, A236800, A236829, A236865, A236915, A236936

Sequence in context: A322865 A238694 A320221 * A236936 A236915 A236865

Adjacent sequences:  A236936 A236937 A236938 * A236940 A236941 A236942

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 01 2014

STATUS

approved

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Last modified July 27 04:55 EDT 2021. Contains 346305 sequences. (Running on oeis4.)