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A365143
Proper dimension of the polyomino with code A365142(n).
1
0, 1, 2, 1, 2, 3, 2, 2, 2, 3, 1, 3, 2, 3, 3, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 4, 1, 2, 3, 4, 4, 4, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 3, 2, 3, 3, 4, 4, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3
OFFSET
1,3
COMMENTS
Can be read as an irregular triangle, whose n-th row contains A005519(n) terms. The first term of the n-th row is A000720(n). The number of times d occurs in the n-th row is A049430(n,d).
FORMULA
a(n) = max_{1<=i<=m} A061395(e_i+1), where A365142(n) = Sum_{1<=i<=m} 2^e_i and e_1 < ... < e_m != 0 (i.e., (e_1, ..., e_m) is the A365142(n)-th row of A133457).
EXAMPLE
As an irregular triangle:
0;
1;
2, 1;
2, 3, 2, 2, 2, 3, 1;
3, 2, 3, 3, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 4, 1, 2;
...
For the 4th row, the seven 4-cell polyominoes, with codes 15, 23, 39, 43, 46, 51, 139 (4th row of A365142), are the L-tetromino, the properly 3-dimensional nonchiral tetracube, the square tetromino, the T-tetromino, the S-tetromino, the properly 3-dimensional chiral tetracube, and the straight tetromino, with proper dimensions 2, 3, 2, 2, 2, 3, 1, respectively.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved