cp's OEIS Frontend

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.

A379747 The number of Hamiltonian cycles with rotational symmetry of order 3 on the triangular grid, n vertices on each side.

This page as a plain text file.
%I A379747 #19 Jan 06 2025 15:13:33
%S A379747 0,1,1,0,2,6,0,52,270,0,17130,189154,0,51417622
%N A379747 The number of Hamiltonian cycles with rotational symmetry of order 3 on the triangular grid, n vertices on each side.
%C A379747 If n = 3*k + 1, then the triangular grid has a central node, so for such n there are no Hamiltonian cycles and a(n) = 0.
%H A379747 Nicolay Avilov, <a href="/A379747/a379747.jpg">Examples of cycles counted by a(1) - a(8)</a>.
%e A379747 a(3) = 1, the only Hamiltonian cycle being the obvious one running around the edge of the triangle;
%e A379747 a(4) = 0 because there are no Hamiltonian cycles;
%e A379747 a(5) = 2 because there are exactly two Hamiltonian cycles.
%Y A379747 Cf. A112676.
%K A379747 nonn,more
%O A379747 1,5
%A A379747 _Nicolay Avilov_, Jan 01 2025
%E A379747 a(9)-a(10) from _Andrey Zabolotskiy_, Jan 02 2025
%E A379747 a(11)-a(13) from _Talmon Silver_, Jan 04 2025
%E A379747 a(14) from _Talmon Silver_, Jan 06 2025