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Number of symmetrical n-celled polyominoes.
2

%I #34 Mar 21 2024 21:00:51

%S 1,1,2,4,7,15,24,53,89,194,323,722,1197,2706,4465,10229,16814,38900,

%T 63721,148808,243006,571937,931305,2207561,3584959,8551309,13851410,

%U 33229843,53694326,129485500,208738348,505796115,813532119,1980023840,3177764415

%N Number of symmetrical n-celled polyominoes.

%H John Mason, <a href="/A259090/b259090.txt">Table of n, a(n) for n = 1..50</a> (This version corrects erroneous values from a(44) onwards in previous version)

%H T. R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy). See page 21. The 15th entry is not included because their value for A000105(15) was incorrect.

%F a(n) = A000105(n) - A006749(n).

%t A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]];

%t A006749 = Cases[Import["https://oeis.org/A006749/b006749.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := A000105[[n + 1]] - A006749[[n]];

%t Array[a, 28] (* _Jean-François Alcover_, Aug 27 2019 *)

%Y Cf. A000105, A006749.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jun 18 2015

%E a(5)-a(6) corrected and a(15)-a(28) from _Andrew Howroyd_, Dec 04 2018

%E a(29) and beyond from _John Mason_, Dec 22 2021