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A236936 Number T(n,k) of equivalence classes of ways of placing k 9 X 9 tiles in an n X n square under all symmetry operations of the square; irregular triangle T(n,k), n>=9, 0<=k<=floor(n/9)^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, 30, 5, 1, 1, 21, 96, 74, 14, 1, 21, 221, 413, 174, 1, 28, 417, 1525, 1234, 1, 28, 705, 4290, 6124, 1, 36, 1107, 10269, 23259, 1, 36, 1638, 21630, 73204, 1, 45, 2334, 41790, 199436 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,6

LINKS

Table of n, a(n) for n=9..66.

Christopher Hunt Gribble, C++ program

Christopher Hunt Gribble, Example graphics

FORMULA

It appears that:

T(n,0) = 1, n>= 9

T(n,1) = (floor((n-9)/2)+1)*(floor((n-9)/2+2))/2, n >= 9

T(c+2*9,2) =  A131474(c+1)*(9-1) + A000217(c+1)*floor(9^2/4) + A014409(c+2), 0 <= c < 9, c even

T(c+2*9,2) = A131474(c+1)*(9-1) + A000217(c+1)*floor((9-1)(9-3)/4) + A014409(c+2), 0 <= c < 9, c odd

T(c+2*9,3) = (c+1)(c+2)/2(2*A002623(c-1)*floor((9-c-1)/2) + A131941(c+1)*floor((9-c)/2)) + S(c+1,3c+2,3), 0 <= c < 9 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

EXAMPLE

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

.\ k  0      1      2      3      4

n

9     1      1

10    1      1

11    1      3

12    1      3

13    1      6

14    1      6

15    1     10

16    1     10

17    1     15

18    1     15     30      5      1

19    1     21     96     74     14

20    1     21    221    413    174

21    1     28    417   1525   1234

22    1     28    705   4290   6124

23    1     36   1107  10269  23259

24    1     36   1638  21630  73204

25    1     45   2334  41790 199436

.

T(18,3) = 5 because the number of equivalence classes of ways of placing 3 9 X 9 square tiles in an 18 X 18 square under all symmetry operations of the square is 5.

CROSSREFS

Cf. A054252, A236679, A236560, A236757, A236800, A236829, A236865, A236915, A236939.

Sequence in context: A238694 A320221 A236939 * A236915 A236865 A236829

Adjacent sequences:  A236933 A236934 A236935 * A236937 A236938 A236939

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 01 2014

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)