A286895 - OEIS

%I #22 Apr 29 2019 06:16:23

%S 1,1,7,1,28,637,1,196,30184,10151428,1,1225,1443001,3461821825,

%T 8308236966001,1,8575,70656628,1186972525900,19948070175962425,

%U 335267157313994232775,1,58996,3460410037,407106879976216,47895307855522569001,5634835073082541702198396,662932711464914589254954278237

%N Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 7 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.

%C Computed using Burnside's orbit-counting lemma.

%H María Merino, <a href="/A286895/b286895.txt">Rows n=0..35 of triangle, flattened</a>

%H M. Merino and I. Unanue, <a href="https://doi.org/10.1387/ekaia.17851">Counting squared grid patterns with Pólya Theory</a>, EKAIA, 34 (2018), 289-316 (in Basque).

%F For even n and m: T(n,m) = (7^(m*n) + 3*7^(m*n/2))/4;

%F for even n and odd m: T(n,m) = (7^(m*n) + 7^((m*n+n)/2) + 2*7^(m*n/2))/4;

%F for odd n and even m: T(n,m) = (7^(m*n) + 7^((m*n+m)/2) + 2*7^(m*n/2))/4;

%F for odd n and m: T(n,m) = (7^(m*n) + 7^((m*n+n)/2) + 7^((m*n+m)/2) + 7^((m*n+1)/2))/4.

%e Triangle begins:

%e ============================================================================

%e n\m |  0  1    2        3             4                 5

%e ----|-----------------------------------------------------------------------

%e 0   |  1

%e 1   |  1  7

%e 2   |  1  28   637

%e 3   |  1  196  30184    10151428

%e 4   |  1  1225 1443001  3461821825    8308236966001

%e 5   |  1  8575 70656628 1186972525900 19948070175962425 335267157313994232775

%e ...

%Y Cf. A225910,  A283432, A283433, A283434, A286893.

%K nonn,tabl

%O 0,3

%A _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 15 2017