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 A068381 #16 Jan 01 2019 06:37:33 %S A068381 12,32,96,648,7736,228424,11974112,1599762776,382467306272, %T A068381 234367651907856,258981528765867728,733498025032488425464, %U A068381 3770347483688546402804760,49588653272896250824990166768 %N A068381 Number of partitions of n X n checkerboard by two edgewise-connected sets which produce the maximum n^2-2n+2 frontier edges between the two sets. %C A068381 Not divided by 4 because that property may not continue. %C A068381 Each partition is counted twice in this sequence. The sequence can be computed by counting Hamiltonian paths on a n-1 x n-1 grid that start at any vertex on the grid boundary and terminate at another boundary vertex. Counts for whether the path starts or terminates on a corner or non-corner need to be computed separately as there are different multiplication factors. - _Andrew Howroyd_, Apr 13 2016 %e A068381 Illustration of a(2)=6*2: %e A068381 __.__ __.__ __.__ __.__ __.__ __.__ %e A068381 |__| | | |__| | __| |__ | |__.__| | | | %e A068381 |__.__| |__.__| |__|__| |__|__| |__.__| |__|__| %e A068381 Illustration of relation of a Hamiltonian path in a 3 x 3 grid to solutions of a(4): %e A068381 .__.__.__.__. .__.__.__.__. .__.__.__.__. .__.__.__.__. %e A068381 .__.__ |__.__.__. | | |__.__. | |__.__.__. | | |__.__. | %e A068381 __.__| <=> | .__.__| | | .__.__| | | .__.__| | | .__.__| | %e A068381 |__.__. | |__.__.__| | |__.__.__| | |__.__. | | |__.__. | %e A068381 |__.__.__.__| |__.__.__.__| |__.__.__|__| |__.__.__|__| %Y A068381 Cf. A068392, A068393. %Y A068381 Cf. A001184, A000532, A121789. %K A068381 nonn %O A068381 2,1 %A A068381 _R. H. Hardin_, Mar 04 2002 %E A068381 a(7)-a(15) from _Andrew Howroyd_, Apr 13 2016