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 A337965 #22 Sep 09 2022 13:21:50 %S A337965 0,1,5,222,22806,2988280,641731574,204154267353 %N A337965 Total number of graceful labelings of cubic graphs with 2n vertices. %C A337965 Consider vertices numbered 0 thru 3n. Add the edges 0--3n, 1--3n, and either 0--(3n-k), 1--(3n-k+1), ... or k--(3n-k) for 2 <= k < 3n. (Altogether (3n-1)!/2 possibilities.) If the resulting graph has 2n vertices of degree 3, and n+1 isolated vertices, we have gracefully labeled a cubic graph of 2n vertices. %e A337965 When n = 3 the five labelings are: %e A337965 0-9, 1-9, 1-8, 2-8, 0-5, 1-5, 2-5, 0-2, 8-9; %e A337965 0-9, 1-9, 1-8, 2-8, 0-5, 5-9, 2-5, 0-2, 1-2; %e A337965 0-9, 1-9, 2-9, 0-6, 1-6, 1-5, 2-5, 0-2, 5-6; %e A337965 0-9, 1-9, 2-9, 1-7, 2-7, 0-4, 4-7, 2-4, 0-1; %e A337965 0-9, 1-9, 2-9, 0-6, 1-6, 2-6, 0-3, 1-3, 2-3. %e A337965 The first four are graceful labelings of the prism K3 x K2. The fifth is a graceful labeling of the utilities graph K3,3. %Y A337965 Cf. A337274, A334613. %K A337965 nonn,more %O A337965 1,3 %A A337965 _Don Knuth_, Oct 05 2020 %E A337965 a(8) from _Bert Dobbelaere_, Sep 09 2022