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 A225202 #19 Aug 24 2023 03:13:51 %S A225202 1,1,2,3,7,9,20,29,52,80,143,217,376,588,977,1563,2583,4116,6764, %T A225202 10854,17688,28512,46367,74763,121385,196040,317756,513616,832039, %U A225202 1345192,2178308,3522981,5702741,9224880,14930324,24153416,39088168,63239220,102333776,165569166,267914295,433476128,701408732 %N A225202 Number of aperiodic tilings of an n X 1 rectangle by tiles of dimension 1 X 1 and 2 X 1. %C A225202 a(n) is the Möbius transform of Fibonacci(n+1). %H A225202 Paul Tek, <a href="/A225202/b225202.txt">Table of n, a(n) for n = 1..1000</a> %H A225202 Paul Tek, <a href="/A225202/a225202_1.png">Illustration of the first terms</a>. %F A225202 a(p)+1 = Fibonacci(p+1) for any prime p. %e A225202 A 4 x 1 rectangle can be tiled in 5 ways: %e A225202 +-+-+-+-+ +---+-+-+ +-+---+-+ +-+-+---+ +---+---+ %e A225202 | | | | | | | | | | | | | | | | | | | | %e A225202 +-+-+-+-+, +---+-+-+, +-+---+-+, +-+-+---+ and +---+---+. %e A225202 The first tiling is 1-periodic, the last tiling is 2-periodic, while the others are not periodic. Hence a(4)=3. %e A225202 Note that although the three remaining tilings are equivalent by circular shift, they are considered as distinct. %t A225202 a[n_] := DivisorSum[n, MoebiusMu[n/#] * Fibonacci[#+1] &]; Array[a, 50] (* _Amiram Eldar_, Aug 22 2023 *) %o A225202 (PARI) a(n)=sumdiv(n,d,moebius(n/d)*fibonacci(d+1)) %Y A225202 Cf. A000045, A001037. %K A225202 nonn %O A225202 1,3 %A A225202 _Paul Tek_, May 01 2013