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Can be read as an irregular triangle, whose n-th row contains A068870(n) terms.

Can be read as an irregular triangle, whose n-th row contains Sum_{d=0..5} A049430(n,d) terms.

The code used here is similar to the binary code defined in A365139, but it is based on an ordering of all sequences of nonnegative integers with a finite number of nonzero terms. The ordering is defined by assigning the ordinal number (Product_{i>=1} prime(i)^x_i) - 1 to the sequence (x_1, x_2, ...). Given a polyomino in any dimension (represented as a finite set of sequences of nonnegative integers with a finite number of nonzero terms, each representing a cell of the polyomino), consider all the ways of rotating/reflecting it. Translate each such rotation/reflection so that the minimum coordinate is 0 in each dimension, and add the powers of 2 with exponents equal to the ordinal numbers of the cells of the translation. The code of the polyomino is the minimum of those sums. The minimum will occur for a transformation for which the largest index of a nonzero coordinate is as small as possible, so only a finite number of transformations need to be considered.

Can be read as an irregular triangle, whose n-th row contains A005519(n) terms. The first term of the n-th row is 2^n-1. For n <= 4, the last term of the n-th row corresponds to the straight n-omino (with code Sum_{j=0..n-1} 2^(2^j-1)), but the last term of the 5th row (133158) corresponds to the x-pentomino, and the last term of the 6th row (576460752840441890) corresponds to the hexacube composed of two straight tricubes orthogonally attached to each other at their middle cubes.