A365143 Proper dimension of the polyomino with code A365142(n).

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

Author

Pontus von Brömssen, Aug 25 2023

Keywords

• nonn
• tabf

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).

Examples

			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.
		

Links

• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A000720, A005519, A049430, A061395, A133457, A365142.

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).