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 A225910 Square array read by antidiagonals: a(m,n) is the number of binary pattern classes in the (m,n)-rectangular grid, two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other. 18
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 6, 7, 6, 1, 1, 10, 24, 24, 10, 1, 1, 20, 76, 168, 76, 20, 1, 1, 36, 288, 1120, 1120, 288, 36, 1, 1, 72, 1072, 8640, 16576, 8640, 1072, 72, 1, 1, 136, 4224, 66816, 263680, 263680, 66816, 4224, 136, 1, 1, 272, 16576, 529920, 4197376, 8407040, 4197376, 529920, 16576, 272, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS In the square table A000012, A005418, and A225826 to A225834 are the first 11 rows (see example). In the square table, m odd (see formula). The order of the recurrence equations is 4. Let it be (a1(m),a2(m),a3(m),a4(m)) the characterizing 4-plet of a(m). The sequence a1(m) belongs to A028403 (2^m+2^((m+1)/2)), -a2(m) to A147538 (2^m*(2^((m+1)/2)-1) and a4(m) to A013824 (2^(2m)*2^((m+1)/2)). -a3(m) sequence formula is 2^m*(2^m+2^((m+1)/2)). All the coefficients of x in generating functions from A225826 to A225834  belong to A113979. LINKS Alois P. Heinz, Antidiagonals n = 0..65, flattened FORMULA m even and n even: a(m,n) = 2^(m*n/2-2)*(2^(m*n/2) + 3); m even and n odd: a(m,n) = 2^(m*n/2-1)*(2^(m*n/2-1) + 2^(m/2-1) + 1); m odd and n even: a(m,n) = 2^(m*n/2-1)*(2^(m*n/2-1) + 2^(n/2-1) + 1); m odd and n odd: a(m,n) = 2^((m*n-1)/2-1)*(2^((m*n-1)/2) + 2^((m-1)/2) + 2^((n-1)/2) + 1). m even: a(m,n) = 2^m*a(m,n-1) + 2^m*a(m,n-2) - (2^m)^2*a(m,n-3) with n>2, a(m,0)=1, a(m,1)=a(1,m), a(m,2)=a(2,m). m odd: a(m,n) = 2^m*a(m,n-1) + 2^m*a(m,n-2) - (2^m)^2*a(m,n-3) - 2^(((m+1)/2)*n-3)*(2^((m-1)/2)-1) with n>2, a(m,0)=1, a(m,1)=a(1,m), a(m,2)=a(2,m). Only a(1,n) and a(2,n) (A005418 and A225826) sequences are needed to define the others. EXAMPLE Array begins: 1   1      1         1            1               1                  1 ... 1   2      3         6           10              20                 36 ... 1   3      7        24           76             288               1072 ... 1   6     24       168         1120            8640              66816 ... 1  10     76      1120        16576          263680            4197376 ... 1  20    288      8640       263680         8407040          268517376 ... 1  36   1072     66816      4197376       268517376        17180065792 ... 1  72   4224    529920     67133440      8590786560      1099516870656 ... 1 136  16576   4212736   1073790976    274882625536     70368756760576 ... 1 272  66048  33632256  17180262400   8796137062400   4503599962914816 ... 1 528 262912 268713984 274878693376 281475261923328 288230376957018112 ... ... CROSSREFS Cf. A005418, A225826-A225834. Sequence in context: A285522 A181039 A215297 * A215292 A124975 A171246 Adjacent sequences:  A225907 A225908 A225909 * A225911 A225912 A225913 KEYWORD nonn,easy,tabl AUTHOR Yosu Yurramendi, May 20 2013 STATUS approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)