login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286920 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 9 colors and n>=m, two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other. 2
1, 1, 9, 1, 45, 1701, 1, 405, 134865, 97135605, 1, 3321, 10766601, 70618411521, 463255079498001, 1, 29889, 871858485, 51473762336565, 3039416437115008521, 179474497026544179696969, 1, 266085, 70607782701, 37523729625344145, 19941610769429949618201, 10597789568841677482963905405, 5632099886234793715531013441442501 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Computed using Burnsides orbit-counting lemma.

LINKS

María Merino, Rows n=0..33 of triangle, flattened

M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).

FORMULA

For even n and m: T(n,m) = (9^(m*n) + 3*9^(m*n/2))/4;

for even n and odd m: T(n,m) = (9^(m*n) + 9^((m*n+n)/2) + 2*9^(m*n/2))/4;

for odd n and even m: T(n,m) = (9^(m*n) + 9^((m*n+m)/2) + 2*9^(m*n/2))/4;

for odd n and m: T(n,m) = (9^(m*n) + 9^((m*n+n)/2) + 9^((m*n+m)/2) + 9^((m*n+1)/2))/4.

EXAMPLE

Triangle begins:

==========================================================

n\m |   0   1     2         3              4

----|-----------------------------------------------------

0   |   1

1   |   1   9

2   |   1   45    1701

3   |   1   405   134865    97135605

4   |   1   3321  10766601  70618411521    463255079498001

...

CROSSREFS

Cf. A225910, A283432, A283433, A283434, A286893, A286895, A286919.

Sequence in context: A283043 A283016 A050303 * A306557 A283060 A283082

Adjacent sequences:  A286917 A286918 A286919 * A286921 A286922 A286923

KEYWORD

nonn,tabl

AUTHOR

María Merino, Imanol Unanue, Yosu Yurramendi, May 16 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)