A370199 a(n) is the number of odd polyominoes with n cells.

0, 1, 3, 11, 35, 108, 380, 1348, 5014, 18223, 67634, 252849, 950346, 3602437, 13697333, 52293534, 200399576, 770410271, 2970369338, 11482572252, 44492417777, 172766286339, 672186167762, 2619985274260, 10228841840226, 39996338183554, 156612016049122

Offset: 1

Author

Joerg Arndt and Hugo Pfoertner, Feb 11 2024

Keywords

• nonn
• hard
• more

Comments

Whether a polyomino is "odd" is determined by the fact that the permutation defined by assigning the positions from row- or column-wise enumeration of its cells on a square grid is an odd permutation. See the description in the 'Ponder This' challenge for the exact definition.

The terms a(1)-a(10) were given in this description, and a(11)-a(20) were in the solution. The larger terms are results of the program that the user "uau" provided in the Mersenne forum.

Links

• IBM Research, Counting odd polyominoes, Ponder This, June 2022 - Challenge.
• IBM Research, Counting odd polyominoes, Ponder This, June 2022 - Solution.
• User uau, C program, post in mersenneforum, Jul 22, 2022.

Crossrefs

Cf. A001168.

Programs

C

See the 'user uau' link.

Formula

a(4*n+2) = A001168(4*n+2)/2.

a(4*n+3) = A001168(4*n+3)/2.