A334307 Number of graceful labelings for the complete tripartite graph K_{1,1,n}.

12, 32, 168, 1152, 9600, 97920, 1491840, 21127680, 377395200, 7605964800, 164457216000, 3935477145600, 102571486617600, 2858053098700800, 85725900868608000, 2745404797943808000, 93266934645620736000, 3356738924418367488000, 127589166595209166848000

Offset: 1

Author

Eric W. Weisstein, Apr 24 2020

Keywords

• nonn

Comments

Except for n = 2, a(n) = A333728(n+2) up to at least n = 6.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..400 (terms 1..48 from Don Knuth)
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph
• Eric Weisstein's World of Mathematics, Graceful Labeling

Crossrefs

Cf. A333728 (maximum number of graceful labelings for an n-node simple graph), A339891.

Programs

Mathematica

A334307[n_]:=If[n==1,12,4n!(DivisorSum[2n+1,2^((#-1)/2)&]+DivisorSigma[0,n+1]-2^(n-1)-1)];Array[A334307, 25] (* Paolo Xausa, Dec 04 2023 *)

Formula

If n>1, a(n) = 4*A339891(n)*n!. - Don Knuth, Dec 21 2020.

Extensions

a(8) and a(9) from Pontus von Brömssen, Jul 25 2020

Terms a(10) and beyond from Don Knuth, Dec 21 2020