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%I #14 Sep 24 2023 11:10:25
%S 1,9,11,19,22,33,37,51,56,73,79,99,106,129,137,163,172,201,211,243,
%T 254,289,301,339,352,393,407,451,466,513,529,579,596,649,667,723,742,
%U 801,821,883,904,969,991,1059,1082,1153,1177,1251,1276,1353,1379,1459,1486,1569,1597,1683,1712,1801,1831
%N Number of distinct tilings of a 2n X 2n square with 1 x n polyominoes.
%C The positions of n X n subsquares greatly restricts which permutations are possible, simplifying finding solutions. a(n+1) - a(n) = A014682 (n+2), where A014682 is the Collatz function, except a(2)-a(1) = 8 and A014682(4) = 5.
%H Jeff Bowermaster, <a href="/A329279/a329279.png">Illustration of a(1)..a(3)</a>
%H Jeff Bowermaster, <a href="/A329279/a329279_1.png">Illustration of a(4) and a(5)</a>
%H Jeff Bowermaster, <a href="/A329279/a329279_2.png">Illustration of a(6)</a>
%H Jeff Bowermaster, <a href="/A329279/a329279_3.png">Illustration of a(7)</a>
%H Jeff Bowermaster, <a href="/A329279/a329279_4.png">Illustration of a(8)</a>
%F For even n, a(n) = (n^2+4n)/2+3; for odd n, a(n) = (n^2+3n)/2+2 ; a(1) = 1.
%o (PARI) a(n) = if(n==1,1,if(n%2,(n^2+3*n)/2+2,(n^2+4*n)/2+3))
%Y Cf. A014682, A060312, A058331 (bisection).
%K nonn
%O 1,2
%A _Jeff Bowermaster_, Nov 11 2019
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