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A349329 Number of polyominoes with 2n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid and passes through the corner of at least one square.

%I A349329 #33 Apr 16 2023 09:23:23
%S A349329 0,0,2,7,28,100,368,1335,4912,18125,67477,252573,951363,3601113,
%T A349329 13695150,52291510,200389661,770391542,2970337861,11482318605,
%U A349329 44491635790,172766013959,672185703574,2619993338628
%N A349329 Number of polyominoes with 2n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid and passes through the corner of at least one square.
%H A349329 John Mason, <a href="/A349329/b349329.txt">Table of n, a(n) for n = 1..50</a>
%F A349329 a(n) = A006746(2n) - A349328(2n).
%F A349329 a(n) = 2*(A006747(n) + A006748(n)) + A144553(n) + A056878(n) + A006746(n) + 4*A006749(n). - corrected by _John Mason_, Feb 26 2023
%e A349329 a(3)=2 because of hexominoes:
%e A349329   OO   and   O
%e A349329   O          OO
%e A349329   O          OO
%e A349329   OO         O
%Y A349329 Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349328.
%K A349329 nonn
%O A349329 1,3
%A A349329 _John Mason_, Nov 15 2021
%E A349329 Name corrected by _John Mason_, Feb 01 2022