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A234006 Free polyominoes with 2n squares, having reflectional symmetry on axis that coincides with edges. 7

%I #46 Apr 16 2023 12:35:34

%S 1,2,4,11,35,114,392,1381,4998,18292,67791,253182,952527,3603389,

%T 13699516,52300071,200406183,770424072,2970400815,11482442855,

%U 44491876993,172766491178,672186631950,2619995178793,10228902801505,39996341268584,156612023001490,614044347934591

%N Free polyominoes with 2n squares, having reflectional symmetry on axis that coincides with edges.

%C The number of free polyominoes of size 2n that have reflectional symmetry on a horizontal or vertical axis that coincides with the edges of some of the squares. The sequence is defined for 2n rather than n as odd-sized polyominoes cannot have the required symmetry.

%H John Mason, <a href="/A234006/b234006.txt">Table of n, a(n) for n = 1..50</a>

%F a(2*n+1) = A151525(2*n+1), a(2*n) = A151525(2*n) + A182645(n) - A001168(n). - _Andrew Howroyd_, Dec 05 2018

%F If n odd, a(n) = A349329(n) + A346799(n), otherwise a(n) = A349329(n) + A346799(n) + A346800(n/2) + A351191(n/2). - _John Mason_, Mar 15 2023

%t A151525 = Cases[Import["https://oeis.org/A151525/b151525.txt", "Table"], {_, _}][[All, 2]];

%t A182645 = Cases[Import["https://oeis.org/A182645/b182645.txt", "Table"], {_, _}][[All, 2]];

%t A001168 = Cases[Import["https://oeis.org/A001168/b001168.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := If[OddQ[n], A151525[[n]], A151525[[n]] + A182645[[n/2]] - A001168[[n/2]]];

%t Array[a, 28] (* _Jean-François Alcover_, Sep 10 2019, after _Andrew Howroyd_ *)

%Y Cf. A000105, A001168, A001933, A151525, A182645, A234007, A234008, A234009, A234010, A349329, A346779, A346800, A351191.

%K nonn

%O 1,2

%A _John Mason_, Dec 18 2013

%E a(12)-a(28) from _Andrew Howroyd_, Dec 05 2018

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)