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 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

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