This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329279 #14 Sep 24 2023 11:10:25 %S A329279 1,9,11,19,22,33,37,51,56,73,79,99,106,129,137,163,172,201,211,243, %T A329279 254,289,301,339,352,393,407,451,466,513,529,579,596,649,667,723,742, %U A329279 801,821,883,904,969,991,1059,1082,1153,1177,1251,1276,1353,1379,1459,1486,1569,1597,1683,1712,1801,1831 %N A329279 Number of distinct tilings of a 2n X 2n square with 1 x n polyominoes. %C A329279 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 A329279 Jeff Bowermaster, <a href="/A329279/a329279.png">Illustration of a(1)..a(3)</a> %H A329279 Jeff Bowermaster, <a href="/A329279/a329279_1.png">Illustration of a(4) and a(5)</a> %H A329279 Jeff Bowermaster, <a href="/A329279/a329279_2.png">Illustration of a(6)</a> %H A329279 Jeff Bowermaster, <a href="/A329279/a329279_3.png">Illustration of a(7)</a> %H A329279 Jeff Bowermaster, <a href="/A329279/a329279_4.png">Illustration of a(8)</a> %F A329279 For even n, a(n) = (n^2+4n)/2+3; for odd n, a(n) = (n^2+3n)/2+2 ; a(1) = 1. %o A329279 (PARI) a(n) = if(n==1,1,if(n%2,(n^2+3*n)/2+2,(n^2+4*n)/2+3)) %Y A329279 Cf. A014682, A060312, A058331 (bisection). %K A329279 nonn %O A329279 1,2 %A A329279 _Jeff Bowermaster_, Nov 11 2019