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A370199
a(n) is the number of odd polyominoes with n cells.
0
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
1,3
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.
FORMULA
a(4*n+2) = A001168(4*n+2)/2.
a(4*n+3) = A001168(4*n+3)/2.
PROG
(C) See the 'user uau' link.
CROSSREFS
Cf. A001168.
Sequence in context: A027060 A171498 A126939 * A126940 A026125 A026154
KEYWORD
nonn,hard,more
AUTHOR
Joerg Arndt and Hugo Pfoertner, Feb 11 2024
STATUS
approved