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A352431 Number T(n,k) of tilings of a 2k X n rectangle using dominoes and 2 X 2 tiles.

%I A352431 #20 Apr 20 2023 14:56:25
%S A352431 1,1,1,1,1,1,1,1,3,1,1,1,11,5,1,1,1,43,29,11,1,1,1,171,173,165,21,1,1,
%T A352431 1,683,1037,2773,593,43,1,1,1,2731,6221,48605,17937,2773,85,1,1,1,
%U A352431 10923,37325,864901,550969,205879,11093,171,1
%N A352431 Number T(n,k) of tilings of a 2k X n rectangle using dominoes and 2 X 2 tiles.
%C A352431 Tiling algorithm, see A351322.
%C A352431 The table is read by descending antidiagonals.
%C A352431 If read by columns or rows:
%C A352431 T(n,1) = A001045(n+1);
%C A352431 T(3,k) = A083066(k);
%C A352431 T(n,2) = A352432(n);
%C A352431 T(5,k) = A352433(k).
%H A352431 Andrew Howroyd, <a href="/A352431/b352431.txt">Table of n, a(n) for n = 0..860</a> (first 41 antidiagonals).
%H A352431 Gerhard Kirchner, <a href="/A352431/a352431.txt">Maxima code</a>
%e A352431 Table T(n,k) begins:
%e A352431   n\k 0   1     2        3          4
%e A352431   -----------------------------------
%e A352431   0:  1   1     1        1          1
%e A352431   1:  1   1     1        1          1
%e A352431   2:  1   3    11       43        171
%e A352431   3:  1   5    29      173       1037
%e A352431   4:  1  11   165     2773      48605
%e A352431   5:  1  21   593    17937     550969
%e A352431   6:  1  43  2773   205879   16231655
%e A352431   7:  1  85 11093  1615993  242436361
%e A352431   8:  1 171 48605 16231655 5811552169
%o A352431 (Maxima) See "Maxima code" link.
%Y A352431 Cf. A351322, A001045, A083066, A352432, A352433.
%K A352431 nonn,tabl
%O A352431 0,9
%A A352431 _Gerhard Kirchner_, Mar 17 2022