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A210996 Number of free polyominoes with 2n cells.

%I A210996 #44 Feb 16 2025 08:33:17
%S A210996 1,1,5,35,369,4655,63600,901971,13079255,192622052,2870671950,
%T A210996 43191857688,654999700403,9999088822075,153511100594603,
%U A210996 2368347037571252,36695016991712879,570694242129491412,8905339105809603405,139377733711832678648,2187263896664830239467,34408176607279501779592
%N A210996 Number of free polyominoes with 2n cells.
%C A210996 It appears that we can write A216492(n) < A216583(n) < A056785(n) < A056786(n) < a(n) < A210988(n) < A210986(n), if n >= 3. - _Omar E. Pol_, Sep 16 2012
%H A210996 John Mason, <a href="/A210996/b210996.txt">Table of n, a(n) for n = 0..25</a>
%H A210996 Herman Tulleken, <a href="https://www.researchgate.net/publication/333296614_Polyominoes">Polyominoes 2.2: How they fit together</a>, (2019).
%H A210996 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polyomino.html">Polyomino</a>
%H A210996 Wikipedia, <a href="http://en.wikipedia.org/wiki/File:Tetramino.png">All 5 free tetrominoes</a>, Illustration of a(2) = 5.
%H A210996 Wikipedia, <a href="http://en.wikipedia.org/wiki/File:All_35_free_hexominoes.svg">All 35 free hexominoes</a>, Illustration of a(3) = 35.
%H A210996 Wikipedia, <a href="http://en.wikipedia.org/wiki/File:The_369_Free_Octominoes.svg">All 369 free octominoes</a>, Illustration of a(4) = 369.
%H A210996 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%F A210996 a(n) = A000105(2n).
%F A210996 a(n) = A213376(n) + A056785(n). - _R. J. Mathar_, Feb 08 2023
%e A210996 For n = 1 there is only one free domino. For n = 2 there are 5 free tetrominoes. For n = 3 there are 35 free hexominoes. For n = 4 there are 369 free octominoes (see link section).
%t A210996 A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]];
%t A210996 Partition[A000105, 2][[All, 1]] (* _Jean-François Alcover_, Jan 03 2020 *)
%Y A210996 Bisection of A000105.
%Y A210996 Cf. A000988, A056785, A056786, A210988, A210997, A216492, A216583.
%K A210996 nonn
%O A210996 0,3
%A A210996 _Omar E. Pol_, Sep 15 2012
%E A210996 More terms from _John Mason_, Apr 15 2023