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 A339891 #40 Feb 16 2025 08:34:01
%S A339891 1,4,7,12,20,34,74,131,260,524,1030,2054,4118,8196,16389,32804,65554,
%T A339891 131074,262216,524292,1048580,2097304,4194312,8388619,16777478,
%U A339891 33554436,67108906,134218244,268435464,536870914,1073742880,2147483720,4294967300,8589936646,17179869193
%N A339891 Number of fundamentally different graceful labelings of the complete tripartite graph K_{1,1,n}.
%C A339891 The difference between "fundamentally different graceful labelings" of a graph and "graceful labelings" of a graph is that the latter is the former multiplied by twice the number of automorphisms. (The extra factor of 2 comes from complementation.)
%C A339891 When n>1, the graph K_{1,1,n} has 2n! automorphisms.
%D A339891 D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3, in preparation.
%H A339891 Paolo Xausa, <a href="/A339891/b339891.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..48 from Don Knuth)
%H A339891 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H A339891 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GracefulLabeling.html">Graceful Labeling</a>
%F A339891 a(n) = A339916(n) + A000005(n+1) - 2^(n-1) - 1 - 2*[n=1].
%t A339891 A339891[n_]:=If[n==1,1,DivisorSum[2n+1,2^((#-1)/2)&]+DivisorSigma[0,n+1]-2^(n-1)-1];Array[A339891,50] (* _Paolo Xausa_, Dec 04 2023 *)
%Y A339891 If n>1, A334307(n) = 4*a(n)*n!.
%K A339891 nonn
%O A339891 1,2
%A A339891 _Don Knuth_, Dec 21 2020