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

1,3

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).

Links

Table of n, a(n) for n=1..87.

Index entries for sequences related to polyominoes.

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

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

Sequence in context: A331084 A067694 A131810 * A233519 A192295 A037195

Adjacent sequences: A365140 A365141 A365142 * A365144 A365145 A365146

Keyword

nonn,tabf

Author

Pontus von Brömssen, Aug 25 2023

Status

approved