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a(n) is the number of odd polyominoes with n cells.
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%I #13 Feb 15 2024 13:28:59

%S 0,1,3,11,35,108,380,1348,5014,18223,67634,252849,950346,3602437,

%T 13697333,52293534,200399576,770410271,2970369338,11482572252,

%U 44492417777,172766286339,672186167762,2619985274260,10228841840226,39996338183554,156612016049122

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

%C 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.

%C 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.

%H IBM Research, <a href="https://research.ibm.com/haifa/ponderthis/challenges/June2022.html">Counting odd polyominoes</a>, Ponder This, June 2022 - Challenge.

%H IBM Research, <a href="https://research.ibm.com/haifa/ponderthis/solutions/June2022.html">Counting odd polyominoes</a>, Ponder This, June 2022 - Solution.

%H User uau, <a href="https://www.mersenneforum.org/showpost.php?p=610016&amp;postcount=10">C program</a>, post in mersenneforum, Jul 22, 2022.

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

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

%o (C) See the 'user uau' link.

%Y Cf. A001168.

%K nonn,hard,more

%O 1,3

%A _Joerg Arndt_ and _Hugo Pfoertner_, Feb 11 2024